Skip to main content Accessibility help
×
Hostname: page-component-848d4c4894-cjp7w Total loading time: 0 Render date: 2024-06-30T22:17:28.237Z Has data issue: false hasContentIssue false

References

Published online by Cambridge University Press:  11 September 2020

Charles R. Johnson
Affiliation:
College of William and Mary, Virginia
Ronald L. Smith
Affiliation:
University of Tennessee, Chattanooga
Michael J. Tsatsomeros
Affiliation:
Washington State University, Pullman, WA
Get access

Summary

Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Chapter
Information
Matrix Positivity , pp. 189 - 205
Publisher: Cambridge University Press
Print publication year: 2020

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[AH08] Alanelli, M. and Hadjidimos, A., A new iterative criterion for H-matrices: the reducible case, Linear Algebra Appl., 428 (2008), 27612777.CrossRefGoogle Scholar
[Al-No88] Al-Nowaihi, A., P-matrices: an equivalent characterization, J. Algebra, 112 (1988), 385387.Google Scholar
[ACE95] Andersson, L., Chang, G. Z., and Elfving, T., Criteria for copositive matrices using simplices and barycentric coordinates, Proceedings of the Workshop on Nonnegative Matrices, Applications and Generalizations and the Eighth Haifa Matrix Theory Conference (Haifa, 1993), Linear Algebra Appl., 220 (1995), 930.CrossRefGoogle Scholar
[And80] Ando, T., Inequalities for M-matrices, Linear Multilinear Algebra, 8 (1979/80), 291316.Google Scholar
[Bal70] Ballantine, C. S., Stabilization by a diagonal matrix, Proceedings of the American Mathematical Society, 25 (1970), 728734.Google Scholar
[BaJoh76] Ballantine, C. S. and Johnson, C. R., Accretive matrix products, Linear Multilinear Algebra, 3 (1975/76), no. 3, 169185.Google Scholar
[BCN05] Bapat, R. B., Catral, M., and Neumann, M., On functions that preserve M-matrices and inverse M-matrices, Linear Multilinear Algebra, 53 (2005), 193201.CrossRefGoogle Scholar
[Bas68] Baston, V. J. D., Extreme copositive quadratic forms, Acta Arith., 15 (1968/1969), 319327.Google Scholar
[Bau66] Baumert, L. D., Extreme copositive quadratic forms, Pacific J. Math., 19 (1966), 197204.Google Scholar
[Bau67] Baumert, L. D., Extreme copositive quadratic forms, II, Pacific J. Math., 20 (1967), 120.Google Scholar
[B-IG03] Ben-Israel, A. and Greville, T. N. E., Generalized Inverses: Theory and Applications, 2nd edition, CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC, 15, New York: Springer-Verlag, 2003.Google Scholar
[BCEM12] Bendito, E., Carmona, A., Encinas, A. M., and Mitjana, M., The M-matrix inverse problem for singular and symmetric Jacobi matrices, Linear Algebra Appl., 436 (2012), 10901098.Google Scholar
[Ber81] Berman, A., Matrices and the linear complementarity problem, Linear Algebra Appl., 40 (1981), 249256.Google Scholar
[BDS15] Berman, A., Dür, M., and Shaked-Monderer, N., Open problems in the theory of completely positive and copositive matrices, Electron. J. Linear Algebra, 29 (2015), 4658.CrossRefGoogle Scholar
[BH83] Berman, A. and Hershkowitz, D., Matrix diagonal stability and its implications, SIAM J. Algebraic Discrete Methods, 4 (1983), 377382.CrossRefGoogle Scholar
[BHJ85] Berman, A., Hershkowitz, D., and Johnson, C. R., Linear transformations that preserve certain positivity classes of matrices, Linear Algebra Appl., 68 (1985), 929.Google Scholar
[BP94] Berman, A. and Plemmons, R. J., Nonnegative Matrices in the Mathematical Sciences, SIAM, Philadelphia, 1994.Google Scholar
[BS-M03] Berman, A. and Shaked-Monderer, N., Completely Positive Matrices, Singapore: World Scientific, 2003.Google Scholar
[BVW78] Berman, A., Varga, R. S., and Ward, R. C., ALPS: matrices with nonpositive off-diagonal entries, Linear Algebra Appl., 21 (1978), 233244.Google Scholar
[BW77] Berman, A. and Ward, R. C., Stability and semipositivity of real matrices, Bull. Amer. Math. Soc., 83 (1977), 262263.Google Scholar
[BW78] Berman, A. and Ward, R. C., ALPS: classes of stable and semipositive matrices, Linear Algebra Appl., 21 (1978), 163174.Google Scholar
[Bha07] Bhatia, R., Positive Definite Matrices, Princeton, NJ: Princeton University Press, 2007.Google Scholar
[BG84] Bialas, S. and Garloff, J., Intervals of P-matrices and related matrices, Linear Algebra Appl., 58 (1984), 3341.CrossRefGoogle Scholar
[Blatt62] Blattner, J. W., Bordered matrices, J. Soc. Indust. Appl. Math., 10 (1962) 528536.Google Scholar
[Bom87] Bomze, I. M., Remarks on the recursive structure of copositivity, J. Inform. Optim. Sci., 8 (1987), 243260.Google Scholar
[Bom96] Bomze, I. M., Block pivoting and shortcut strategies for detecting copositivity, Linear Algebra Appl., 248 (1996), 161184.Google Scholar
[Bom00] Bomze, I. M., Linear-time copositivity detection for tridiagonal matrices and extension to block-tridiagonality, SIAM J. Matrix Anal. Appl., 21 (2000), 840848.Google Scholar
[Bom08] Bomze, I. M., Perron–Frobenius property of copositive matrices, and a block copositivity criterion, Linear Algebra Appl., 429 (2008), 6871.Google Scholar
[BEFB94] Boyd, S., El Ghaoui, L., Feron, E., and Balakrishnan, V., Linear Matrix Inequalities in System and Control Theory, Philadelphia: SIAM, 1994.Google Scholar
[BPS05] Bru, R., Pedroche, F., and Szyld, D., Subdirect sums of nonsingular M-matrices and of their inverses, Electron. J. Linear Algebra, 13 (2005), 162174.Google Scholar
[Car67] Carlson, D., Weakly sign-symmetric matrices and some determinantal inequalities, Colloq. Math., 17 (1967), 123129.Google Scholar
[CM] Carlson, D. and Markham, T., Products of inverse M-matrices, working paper.Google Scholar
[CS94] Chang, G. and Sederberg, T. W., Nonnegative quadratic Bézier triangular patches, Comput. Aided Geom. Design, 11 (1994), 113116.Google Scholar
[CLW12] Chen, F., Li, Y., and Wang, D., A new eigenvalue bound for the Hadamard product of an M-matrix and an inverse M-matrix, Electron. J. Linear Algebra, 23 (2012), 287294.Google Scholar
[Che04a] Chen, S., A property concerning the Hadamard powers of inverse M-matrices, Linear Algebra Appl., 381 (2004), 5360.Google Scholar
[Che04b] Chen, S., A lower bound for the minimum eigenvalue of the Hadamard product of matrices, Linear Algebra Appl., 378 (2004), 159166.Google Scholar
[Che07a] Chen, S., Proof of a conjecture concerning the Hadamard powers of inverse M-matrices, Linear Algebra Appl., 422 (2007), 477481.Google Scholar
[Che07b] Chen, S., Inequalities for M-matrices and inverse M-matrices, Linear Algebra Appl., 426 (2007), 610618.CrossRefGoogle Scholar
[CSY01] Chen, X., Shogenji, Y., and Yamasaki, M., Verification for existence of solutions of linear complementarity problems, Linear Algebra Appl., 324 (2001), 1526.Google Scholar
[CKL92] Cho, S. J., Kye, S., and Lee, S. G., Generalized Choi maps in three-dimensional matrix algebra, Linear Algebra Appl., 171 (1992), 213224.Google Scholar
[Choi75] Choi, M.-D., Positive semidefinite biquadratic forms, Linear Algebra Appl., 12 (1975), 95100.CrossRefGoogle Scholar
[CKS18a] Choudhury, P. N., Kannan, R., and Sivakumar, K. C., A note on linear preservers of semipositive and minimally semipositive matrices, Electron. J. Linear Alg., 34 (2018), 687694.Google Scholar
[Cott10] Cottle, R. W., A field guide to the matrix classes found in the literature of the linear complementarity problem, J. Glob. Optim., 46 (2010), 571580.Google Scholar
[CHL70a] Cottle, R. W., Habetler, G. J., and Lemke, C. E., Quadratic forms semidefinite over convex cones, In Proceedings of the Princeton Symposium on Mathematical Programming, Princeton, NJ: Princeton University Press, 1970, 551565.Google Scholar
[CHL70b] Cottle, R. W., Habetler, G. J., and Lemke, C. E., On classes of copositive matrices, Linear Algebra Appl., 3 (1970), 295310.Google Scholar
[CPS92] Cottle, R. W., Pang, J.-S., and Stone, R. E., The Linear Complementarity Problem, Boston: Academic Press, 1992.Google Scholar
[Cox94] Coxson, G. E., The P-matrix problem is co-NP-complete, Mathematical Programming, 64 (1994), 173178.Google Scholar
[Cox99] Coxson, G. E., Computing exact bounds on elements of an inverse interval matrix is NP-hard, Reliable Computing, 5 (1999), 137142.Google Scholar
[CH69] Crabtree, D. and Haynsworth, E. V., An identity for the Schur complement of a matrix, Proc. AMS, 22 (1969), 364366.Google Scholar
[CFJ01] Crans, A., Fallat, S., and Johnson, C. R., The Hadamard core of the totally nonnegative matrices, Linear Algebra Appl., 328 (2001), 203222.Google Scholar
[Cry76] Cryer, C. W.. Some properties of totally positive matrices, Linear Algebra Appl., 15 (1976), 125.Google Scholar
[Dan90] Danninger, G., A recursive algorithm for determining (strict) copositivity of a symmetric matrix, Proceedings of the 14th Symposium on Operations Research (Ulm, 1989), Methods Oper. Res., 62, Frankfurt am Main: Hain 45–52.Google Scholar
[DH00] DeAlba, L. M. and Hogben, L., Completions of P-matrix patterns, Linear Algebra Appl., 319 (2000), 83102.Google Scholar
[DMS09] Dellacherie, C., Martinez, S., and San Martin, J., Hadamard functions of inverse M-matrices, SIAM J. Matrix Anal. Appl., 31 (2009), 289315.Google Scholar
[DMS13] Dellacherie, C., Martinez, S., and San Martin, J., The class of inverse M-matrices associated to random walks, SIAM J. Matrix Anal. Appl., 34 (2013), 831854.CrossRefGoogle Scholar
[Dia62] Diananda, P. H., On nonnegative forms in real variables some or all of which are nonnegative, Proc. Cambridge Philos. Soc., 58 (1962), 1725.Google Scholar
[Dic10] Dickinson, P. J. C., An improved characterization of the interior of the completely positive cone, Electron. J. Linear Algebra, 20 (2010), 723729.CrossRefGoogle Scholar
[Dic11] Dickinson, P. J. C., Geometry of the copositive and completely positive cones, J. Math. Anal. Appl., 380 (2011), 377395.Google Scholar
[DDGH13a] Dickinson, P. J. C., Dür, M., Gijben, L., and Hildebrand, R., Irreducible elements of the copositive cone, Linear Algebra Appl., 439 (2013), no. 6, 16051626.Google Scholar
[DDGH13b] Dickinson, P. J. C., Dür, M., Gijben, L., and Hildebrand, R., Scaling relationship between the copositive cone and Parrilo’s first level approximation, Optim. Lett., 7 (2013), no. 8, 16691679.Google Scholar
[DH16] Dickinson, P. J. C. and Hildebrand, R., Considering copositivity locally, J. Math. Anal. Appl., 437 (2016), no. 2, 11841195.Google Scholar
[DLQ18] Ding, W., Luo, Z., and Qi, L., P-tensors, P0 -tensors, and their applications, Linear Algebra Appl., 555 (2018), 336354.Google Scholar
[DGJJT16] Dorsey, J., Gannon, T., Jacobson, N., Johnson, C. R., and Turnansky, M., Linear preservers of semi-positive matrices, Linear Multilinear Algebra, 64 (2016), no. 9, 18531862.Google Scholar
[DGJT16] Dorsey, J., Gannon, T., Johnson, C. R., and Turnansky, M., New results about semipositive matrices, Czechoslovak Math. Journal, 66 (2016), no. 3, 621632.Google Scholar
[Dur10] Dür, M., Copositive Programming – A Survey, In M. Diehl, F. Glineur, Elias Jarlebring, and W. Michiels, Editors, Recent Advances in Optimization and Its Applications in Engineering, pp. 3–20, New York: Springer, 2010.Google Scholar
[E] Engel, G. M., personal communication.Google Scholar
[Gha90] El Ghaoui, L., Robustness of Linear Systems to Parameter Variations, Ph.D. Dissertation, Stanford University, 1990.Google Scholar
[EMS02] Elsner, L., Monov, V., and Szulc, T., On some properties of convex matrix sets characterized by P-matrices and block P-matrices, Linear Multilinear Algebra, 50 (2002), 199218.Google Scholar
[ENN98] Elsner, L., Nabben, R., and Neumann, M., Orthogonal bases that lead to symmetric nonnegative matrices. Linear Algebra Appl., 271 (1998), 323343.Google Scholar
[ES98] Elsner, L. and Szulc, T., Block P-matrices, Linear Multilinear Algebra, 44 (1998), 112.Google Scholar
[ES00] Elsner, L. and Szulc, T., Convex sets of Schur stable and stable matrices, Linear Multilinear Algebra, 48 (2000), 119.Google Scholar
[ES76] Engel, G. M. and Schneider, H., The Hadamard–Fischer inequality for a class of matrices defined by eigenvalue monotonicity, Linear Multilinear Algebra, 4 (1976), 155176.Google Scholar
[EJ91] Eschenbach, C. A. and Johnson, C. R., Sign patterns that require real, nonreal or pure imaginary eigenvalues, Linear Multilinear Algebra, 29 (1991), 299311.Google Scholar
[Fal01] Fallat, S. M., Bidiagonal factorizations of totally nonnegative matrices, American Mathematical Monthly, 108 (2001), 697712.Google Scholar
[FHJ98] Fallat, S. M., Hall, H. T., and Johnson, C. R., Characterization of product inequalities for principal minors of M-matrices and inverse M-matrices, Quart. J. Math. Oxford Ser., (2), 49 (1998), 451458.Google Scholar
[FJ11] Fallat, S. M. and Johnson, C. R., Totally Nonnegative Matrices, Princeton, NJ: Princeton University Press, 2011.Google Scholar
[FJSvdD98] Fallat, S. M., Johnson, C. R., Smith, R. L., and van den Driessche, P., Eigenvalue location for nonnegative and Z-matrices. Linear Algebra Appl., 277 (1998), 187198.Google Scholar
[FJTU00] Fallat, S. M., Johnson, C. R., Torregrosa, J. R., and Urbano, A. M., P-matrix completions under weak symmetry assumptions, Linear Algebra Appl., 312 (2000), 7391.Google Scholar
[FT02] Fallat, S. M. and Tsatsomeros, M. J., On the Cayley transform of certain positivity classes of matrices, Electron. J. Linear Algebra, 9 (2002), 190196.Google Scholar
[Fan60] Fan, K., Note on M-matrices, Quart. J. Math Oxford Ser., (2), 11 (1960), 3–49.CrossRefGoogle Scholar
[Fang89] Fang, L., On the spectra of P- and P0 -matrices, Linear Algebra Appl., 119 (1989), 125.Google Scholar
[FP1912] Fekete, M. and Pólya, G., Über ein problem von Laguerre, Rendiconti del Circolo Matematico di Palermo, 34 (1912), 89100, 110–120.CrossRefGoogle Scholar
[Fie76] Fiedler, M., Aggregation in graphs, Combinatorics, 18 (1976), 315330.Google Scholar
[Fie86] Fiedler, M., Special Matrices and Their Applications in Numerical Mathematics, Leiden, Netherlands: Martinus Nijhoff Publishers, 1986.Google Scholar
[Fie98a] Fiedler, M., Ultrametric matrices in Euclidean point spaces, Electron. J. Linear Algebra, 3 (1998), 2330.CrossRefGoogle Scholar
[Fie98b] Fiedler, M., Some characterizations of symmetric inverse M-matrices, Linear Algebra Appl., 275/276 (1998), 179187.Google Scholar
[Fie00] Fiedler, M., Special ultrametric matrices and graphs, SIAM J. Matrix Anal. Appl., 22 (2000), 106113.Google Scholar
[FJM87] Fiedler, M., Johnson, C. R., and Markham, T. L., Notes on inverse M-matrices, Linear Algebra Appl., 91 (1987), 7581.Google Scholar
[FJMN85] Fiedler, M., Johnson, C. R., Markham, T. L., and Neumann, M., A trace inequality for M-matrices and the symmetrizability of a real matrix by a positive diagonal matrix, Linear Algebra Appl., 71 (1985), 8194.Google Scholar
[FM88a] Fiedler, M. and Markham, T. L., An inequality for the Hadamard product of an M-matrix and an inverse M-matrix, Linear Algebra Appl., 101 (1988), 18.Google Scholar
[FM88b] Fiedler, M. and Markham, T. L., A characterization of the closure of inverse M-matrices, Linear Algebra Appl., 105 (1988), 209223.Google Scholar
[FM90] Fiedler, M. and Markham, T. L., Some connections between the Drazin inverse, P-matrices, and the closure of inverse M-matrices, Linear Algebra Appl., 132 (1990), 163172.Google Scholar
[FM92] Fiedler, M. and Markham, T. L., A classification of matrices of class Z, Linear Algebra Appl., 173 (1992), 115124.CrossRefGoogle Scholar
[FMN83] Fiedler, M., Markham, T. L., and Neumann, M., Classes of products of M-matrices and inverse M-matrices, Linear Algebra Appl., 52/53 (1983), 265287.Google Scholar
[FP62] Fiedler, M. and Pták, V., On matrices with non-positive off-diagonal elements and positive principal minors, Czech. Math. J., 12 (1962), 382400.Google Scholar
[FP66] Fiedler, M. and Pták, V., Some generalizations of positive definiteness and monotonicity, Numerische Mathematik, 9 (1966), 163172.Google Scholar
[FP67] Fiedler, M. and Pták, V., Diagonally dominant matrices, Czech. Math. J., 17 (1967), 420433.CrossRefGoogle Scholar
[FF58] Fischer, M. E. and Fuller, A. T., On the stabilization of matrices and the convergence of linear iterative processes, Proc. Cambridge Philos. Soc., 54 (1958), 417425.Google Scholar
[FHS87] Friedland, S., Hershkowitz, D., and Schneider, H., Matrices whose powers are M-matrices or Z-matrices, Transactions of the American Mathematical Society, 300 (1987), 343366.Google Scholar
[FJZ19] Furtado, S., Johnson, C. R., and Zhang, Y., Linear preservers of copositive matrices, Preprint, 2019.Google Scholar
[Gad58] Gaddum, J. W., Linear inequalities and quadratic forms, Pacific J. Math., 8 (1958), 411414.Google Scholar
[GN65] Gale, D. and Nikaido, H., The Jacobian matrix and global univalence of mappings, Math Ann., 159 (1965), 8193.Google Scholar
[Gan59] Gantmacher, F. R., The Theory of Matrices, Vol. I, New York: Chelsea, 1959.Google Scholar
[GK1935] Gantmacher, F. R. and Krein, M. G., Sur les matrices oscillatoires, Comptes Rendus Mathématique Académie des Sciences Paris, 201 (1935), 577579.Google Scholar
[GZ79] Garcia, C. B. and Zangwill, W. I., On univalence and P-matrices, Linear Algebra Appl., 24 (1979), 239250.Google Scholar
[Gar] Garloff, J., private communication.Google Scholar
[Gar82] Garloff, J., Criteria for Sign Regularity of Sets of matrices, Linear Algebra Appl., 44 (1982), 153160.Google Scholar
[Gar96] Garloff, J., Vertex Implications for Totally Nonnegative Matrices, in Total Positivity and Its Applications, Gasca, M. and Micchelli, C. A., Editors, Boston: Kluwer Academic, 1996, 103107.Google Scholar
[GP96] Gasca, M. and Peña, J. M., On factorizations of totally positive matrices, In M. Gasca and C. A. Micchelli, Editors, Total Positivity and Its Applications (Mathematics and Its Applications), Boston: Kluwer Academic, 359, 1996, 109–130.Google Scholar
[GG19] Gharbia, I. B. and Gilbert, J. C., An algorithmic characterization of P-matricity II: Adjustments, refinements, and validation, SIAM J. Matrix Anal. Appl., 40 (2019), 800813.Google Scholar
[GS14] Goldberg, F. and Shaked-Monderer, N., On the maximal angle between copositive matrices, Electron. J. Linear Algebra, 27 (2014), 837850.Google Scholar
[Gol80] Golumbic, M. C., Algorithmic Graph Theory and Perfect Graphs, New York: Academic Press, 1980.Google Scholar
[Gow89] Gowda, M. S., Pseudomonotone and copositive star matrices, Linear Algebra Appl., 113 (1989), 107118.Google Scholar
[Gow12] Gowda, M. S., On copositive and completely positive cones, and Z-transformations, Electron. J. Linear Algebra, 23 (2012), 198211.Google Scholar
[GR00] Gowda, M. S. and Ravindran, G., Algebraic univalence theorems for nonsmooth functions, J. Math. Anal. Appl., 252 (2000), 917935.Google Scholar
[GS06] Gowda, M. S. and Sznajder, R., Automorphism invariance of P- and GUS-properties of linear transformations on Euclidean Jordan algebras, Mathematics of Operations Research, 31 (2006), 109123.Google Scholar
[GST04] Gowda, M. S., Sznajder, R., and Tao, J., Some P-properties for linear transformations on Euclidean Jordan algebras, Linear Algebra Appl., 393 (2004), 203232.Google Scholar
[GTR12] Gowda, M. S., Tao, J., and Ravindran, G., On the P-property of Z and Lyapunov-like transformations on Euclidean Jordan algebras, Linear Algebra Appl., 436 (2012), 22012209.CrossRefGoogle Scholar
[GT06a] Griffin, K. and Tsatsomeros, M., Principal minors, Part I: A method for computing all the principal minors of a matrix, Linear Algebra Appl., 419 (2006), 107124.Google Scholar
[GT06b] Griffin, K. and Tsatsomeros, M., Principal minors, Part II: The principal minor assignment problem, Linear Algebra Appl., 419 (2006), 125171.Google Scholar
[GJSW84] Grone, R., Johnson, C. R., de Sa, E. M., and Wolkowicz, H., Positive definite completions of partial Hermitian matrices, Linear Algebra Appl., 58 (1984), 109124.Google Scholar
[Had83] Hadeler, K. P., On copositive matrices, Linear Algebra Appl., 49 (1983), 7989.Google Scholar
[Had97] Hadjicostas, P., Copositive matrices and Simpson’s paradox, Linear Algebra Appl., 264 (1997), 475488.Google Scholar
[Hal67] Hall, M., Jr., Combinatorial Theory, 2nd edition, Waltham, MA: Blais-dell Publishing Co., 1967.Google Scholar
[HN63] Hall, M., Jr. and Newman, M., Copositive and completely positive quadratic forms, Proc. Cambridge Philos. Soc., 59 (1963), 329339.CrossRefGoogle Scholar
[Hay68] Haynsworth, E., Determination of the inertia of a partitioned Hermitian matrix, Linear Algebra Appl., 1 (1968), 7381.Google Scholar
[HH69] Haynsworth, E. and Hoffman, A. J., Two remarks on copositive matrices, Linear Algebra Appl., 2 (1969), 387392.Google Scholar
[Hel1923] Helly, E., Über Mengen konvexer Körper mit gemeinschaftlichen Punkte, Jahresbericht der Deutschen Mathematiker-Vereinigung, 32 (1923), 175176.Google Scholar
[Her83] Hershkowitz, D., On the spectra of matrices having nonnegative sums of principal minors, Linear Algebra Appl., 55 (1983), 8186.Google Scholar
[HB83] Hershkowitz, D. and Berman, A., Localization of the spectra of P- and P0 -matrices, Linear Algebra Appl., 52/53 (1983), 383397.Google Scholar
[HJ86a] Hershkowitz, D. and Johnson, C. R., Linear transformations that map the P-matrices into themselves, Linear Algebra Appl., 74 (1986), 2338.Google Scholar
[HJ86b] Hershkowitz, D. and Johnson, C. R., Spectra of matrices with P-matrix powers, Linear Algebra Appl., 80 (1986), 159171.Google Scholar
[HK03] Hershkowitz, D. and Keller, N., Positivity of principal minors, sign symmetry and stability, Linear Algebra Appl., 364 (2003), 105124.Google Scholar
[HS86] Hershkowitz, D. and Schneider, H., Matrices with a sequence of accretive powers, Israel Journal of Mathematics, 55 (1986), 327344.Google Scholar
[Hil12] Hildebrand, R., The extreme rays of the 5 × 5 copositive cone, Linear Algebra Appl., 437 (2012), no. 7, 15381547.Google Scholar
[Hil14] Hildebrand, R., Minimal zeros of copositive matrices, Linear Algebra Appl., 459 (2014), 154174.Google Scholar
[HS10] Hiriart-Urruty, J. B. and Seeger, A., A variational approach to copositive matrices, SIAM Rev., 52 (2010), 593629.Google Scholar
[HP73] Hoffman, A. J. and Pereira, F., On copositive matrices with −1, 0, 1 entries, J. Combinatorial Theory Ser. A, 14 (1973), 302309.Google Scholar
[Hog98a] Hogben, L., Completions of inverse M-matrix patterns, Linear Algebra Appl., 282 (1998), 145160.Google Scholar
[Hog98b] Hogben, L., Completions of M-matrix patterns, Linear Algebra Appl., 285 (1998), 143152.Google Scholar
[Hndbk06] Hogben, L. (Ed.), Handbook of Linear Algebra, Boca Raton, FL: CRC Press Inc., 2006.Google Scholar
[Hog07] Hogben, L., The copositive completion problem: unspecified diagonal entries, Linear Algebra Appl., 420 (2007), no. 1, 160162.Google Scholar
[HJR05] Hogben, L., Johnson, C. R., and Reams, R., The copositive completion problem, Linear Algebra Appl., 408 (2005), 207211.Google Scholar
[Hol05] Holtz, O., M-matrices satisfy Newton’s inequalities, Proc. Amer. Math. Soc., 133 (2005), 711717.Google Scholar
[Hor90] Horn, R. A., The Hadamard product, in Proc. Symp. Appl. Math., Amer. Math. Soc., 40 (1990), 87–169.Google Scholar
[HJ85] Horn, R. A. and Johnson, C. R., Matrix Analysis, New York: Cambridge University Press, 1985.Google Scholar
[HJ91] Horn, R. A. and Johnson, C. R., Topics in Matrix Analysis, New York: Cambridge University Press, 1991.Google Scholar
[HJ13] Horn, R. A. and Johnson, C. R., Matrix Analysis, 2nd edition, New York: Cambridge University Press, 2013.Google Scholar
[HLS10] Huang, R., Liu, J., and Sze, N.-S., Characterizations of inverse M-matrices with special zero patterns, Linear Algebra Appl., 433 (2010), 9941000.Google Scholar
[Ikr02] Ikramov, K. D., An algorithm, linear with respect to time, for verifying the copositivity of an acyclic matrix, Comput. Math. Math. Phys., 42 (2002), 17011703.Google Scholar
[IS00] Ikramov, K. D. and Savel’eva, N. V., Conditionally definite matrices, J. Math, Sci., 98 (2000), 1–50.Google Scholar
[Ima83] Imam, I. N., Tridiagonal and upper triangular inverse M-matrices, Linear Algebra Appl., 55 (1983), 93104.Google Scholar
[Ima84] Imam, I. N., The Schur complement and the inverse M-matrix problem, Linear Algebra Appl., 62 (1984), 235240.Google Scholar
[JJP98] James, G., Johnson, C. R., and Pierce, S., Generalized matrix function inequalities on M-matrices, J. London Math. Soc., 57 (1998), 562582.Google Scholar
[JR99] Jansson, C. and Rohn, J., An algorithm for checking regularity of interval matrices, SIAM Journal Matrix Anal. Appl., 20 (1999), 756776.Google Scholar
[Jar13] Jargalsaikhan, B., Indefinite copositive matrices with exactly one positive eigenvalue or exactly one negative eigenvalue, Electron. J. Linear Algebra, 26 (2013), 754761.Google Scholar
[Joh70] Johnson, C. R., Positive definite matrices, American Mathematical Monthly, 77 (1970), 259264.Google Scholar
[Joh72] Johnson, C. R., Matrices whose Hermitian Part is Positive Definite, PhD thesis, California Institute of Technology (1972).Google Scholar
[Joh73] Johnson, C. R., An inequality for matrices whose symmetric part is positive definite, Linear Algebra Appl., 6 (1973), 1318.Google Scholar
[Joh75a] Johnson, C. R., Inequalities for a complex matrix whose real part is positive definite, Trans. AMS, 212 (1975), 149154.CrossRefGoogle Scholar
[Joh75b] Johnson, C. R., Hadamard’s inequality for matrices with positive definite Hermitian component, Michigan Mathematical Journal, 22 (1975), no. 3, 225228.Google Scholar
[Joh75c] Johnson, C. R., Powers of matrices with positive definite real part, Proc. AMS, 50 (1975), 8591.Google Scholar
[Joh77] Johnson, C. R., A Hadamard product involving M-matrices, Linear Multilinear Algebra, 4 (1976/77), 261264.Google Scholar
[Joh78] Johnson, C. R., Partitioned and Hadamard product matrix inequalities, J. Res. Nat. Bur. Standards, 83 (1978), 585591.Google Scholar
[Joh82] Johnson, C. R., Inverse M-matrices, Linear Algebra Appl., 47 (1982), 195216.Google Scholar
[Joh83] Johnson, C. R., Sign patterns of inverse nonnegative matrices, Linear Algebra Appl., 55 (1983), 6980.Google Scholar
[Joh87] Johnson, C. R., Closure properties of certain positivity classes of matrices under various algebraic operations, Linear Algebra Appl., 97 (1987), 243247.Google Scholar
[Joh90] Johnson, C. R., Matrix completion problems: A survey, In Proc. Symp. Appl. Math., Amer. Math. Soc. 40 (1990), 171–198.Google Scholar
[Joh98] Johnson, C. R., Olga, matrix theory and the Taussky unification problem, Linear Algebra Appl., 280 (1998), 3949.Google Scholar
[JKS94] Johnson, C. R., Kerr, M. K., and Stanford, D. P., Semipositivity of matrices, Linear Multilinear Algebra, 37 (1994), 265271.Google Scholar
[JK96] Johnson, C. R. and Kroschel, B. K., The combinatorially symmetric P-matrix completion problem, Electron. J. Linear Algebra, 1 (1996), 5963.Google Scholar
[JL92] Johnson, C. R., Lundquist, M., Operator matrices with chordal inverse patterns, Operator Theory: Adv. Appl., 59 (1992), 234251.Google Scholar
[JMP09] Johnson, C. R., Marijuan, C., and Pisonero, M., Matrices and spectra satisfying the Newton inequalities, Linear Algebra Appl., 430 (2009), 30303046.Google Scholar
[JMS95] Johnson, C. R., McCuaig, W. D., and Stanford, D. P., Sign patterns that allow minimal semipositivity, Special issue honoring Miroslav Fiedler and Vlastimil Ptak, Linear Algebra Appl., 223/224 (1995), 363373.Google Scholar
[JN13] Johnson, C. R. and Narayan, S. K., When the positivity of the leading principal minors implies the positivity of all principal minors of a matrix, Linear Algebra Appl., 439(2013), 29342947.Google Scholar
[JNT96] Johnson, C. R., Neumann, M., and Tsatsomeros, M., Conditions for the positivity of determinants, Linear Multilinear Algebra, 40 (1996), 241248.Google Scholar
[JO05] Johnson, C. R. and Olesky, D. D., Rectangular submatrices of inverse M-matrices and the decomposition of a positive matrix as a sum, Linear Algebra Appl., 409 (2005), 8799.Google Scholar
[JOTvdD93] Johnson, C. R., Olesky, D. D., Tsatsomeros, M., and van den Driessche, P., Spectra with positive elementary symmetric functions, Linear Algebra Appl., 180 (1993), 247261.Google Scholar
[JOvdD03] Johnson, C. R., Olesky, D. D., and van den Driessche, P., Matrix classes that generate all matrices with positive determinant, SIAM J. Matrix Anal. Appl., 25 (2003), 285294.Google Scholar
[JOvdD95] Johnson, C. R., Olesky, D. D., and van den Driessche, P., Sign determinancy in LU factorization of P-matrices, Linear Algebra Appl., 217 (1995), 155166.Google Scholar
[JOvdD01] Johnson, C. R., Olesky, D. D., and van den Driessche, P., Successively ordered elementary bidiagonal factorization, SIAM J. Matrix Anal. Appl. 22 (2001), 10791088.Google Scholar
[JOvdD03] Johnson, C. R., Olesky, D. D., and van den Driessche, P., Matrix classes that generate all matrices with positive determinant, SIAM J. Matrix Anal. Appl., 25 (2003), 285294.Google Scholar
[JR05] Johnson, C. R. and Reams, R., Spectral theory of copositive matrices, Linear Algebra Appl., 395 (2005), 275281.Google Scholar
[JR08] Johnson, C. R. and Reams, R., Constructing copositive matrices from interior matrices, Electron. J. Linear Algebra, 17 (2008), 920.Google Scholar
[JS96] Johnson, C. R. and Smith, R. L., The completion problem for M-matrices and inverse M-matrices, Linear Algebra Appl., 241–243 (1996), 655667.Google Scholar
[JS99] Johnson, C. R. and Smith, R. L., The symmetric inverse M-matrix completion problem, Linear Algebra Appl., 290 (1999), 193212.Google Scholar
[JS01a] Johnson, C. R. and Smith, R. L., Path product matrices, Linear Multilinear Algebra, 46 (1999), 177191.Google Scholar
[JS01b] Johnson, C. R. and Smith, R. L., Almost principal minors of inverse M-matrices, Linear Algebra Appl., 337 (2001), 253265.Google Scholar
[JS01c] Johnson, C. R. and Smith, R. L., Linear interpolation problems for matrix classes and a transformational characterization of M-matrices, Linear Algebra Appl., 330 (2001), 4348.Google Scholar
[JS02] Johnson, C. R. and Smith, R. L., Intervals of inverse M-matrices, Reliab. Comput., 8 (2002), 239243.Google Scholar
[JS07a] Johnson, C. R. and Smith, R. L., Positive, path product, and inverse M-matrices, Linear Algebra Appl., 421 (2007), 328337.Google Scholar
[JS07b] Johnson, C. R. and Smith, R. L., Path product matrices and eventually inverse M-matrices, SIAM J. Matrix Anal. Appl., 29 (2007), 370376.Google Scholar
[JS11] Johnson, C. R. and Smith, R. L., Inverse M-matrices, II, Linear Algebra Appl., 435 (2011), 953983.Google Scholar
[JS93] Johnson, C. R. and Stanford, D. P., Qualitative semipositivity, Combinatorial and graph-theoretical problems in linear algebra, IMA Vol. Math. Appl., 50 (1993), 99105.Google Scholar
[JT11] Johnson, C. R. and Tong, Z., Equilibrants, semipositive matrices, calculation and scaling, Linear Algebra Appl., 434 (2011), 16381647.Google Scholar
[JT95] Johnson, C. R. and Tsatsomeros, M. J., Convex sets of nonsingular and P-matrices, Linear Multilinear Algebra, 38 (1995), 233239.Google Scholar
[JX93] Johnson, C. R. and Xenophontos, C., Irreducibilty and primitivity of Perron complements: applications of the compressed directed graph, in Graph Theory and Sparse Matrix Computation, IMA Vol. Math. Appl., 56 (1993), 101106.Google Scholar
[JTU02] Jordán, C., Torregrosa, J. R., and Urbano, A. M., Inverse M-matrix completion problem with zeros in the inverse completion, Appl. Math. Lett., 15 (2002), 677684.Google Scholar
[KS14] Rajesh Kannan, M. and Sivakumar, K. C., P -matrices: a generalization of P-matrices, Linear Multilinear Algebra, 62 (2014), 112.Google Scholar
[Kap00] Kaplan, W., A test for copositive matrices, Linear Algebra Appl., 313 (2000), 203206.Google Scholar
[Kap01] Kaplan, W., A copositivity probe, Linear Algebra Appl., 337 (2001), 237251.Google Scholar
[Kel69] Keller, E. L., Quadratic Optimization and Linear Complementarity, Ph.D. thesis, University of Michigan, Ann Arbor, 1969.Google Scholar
[Kel72] Kellogg, R., On complex eigenvalues of M and P matrices, Numer. Math., 19 (1972), 170175.Google Scholar
[KB85] Kessler, O. and Berman, A., Matrices with a transitive graph and inverse M-matrices, Linear Algebra Appl., 71 (1985), 175185.Google Scholar
[KOSvdD06] Kim, I. J., Olesky, D. D., Shader, B. L., and van den Driessche, P., Sign patterns that allow a positive or nonnegative left Inverse, SIAM J. Matrix Anal. Appl., 29 (2007), 554565.Google Scholar
[KN91] Koltracht, I. and Neumann, M., On the inverse M-matrix problem for real symmetric positive-definite Toeplitz matrices, SIAM J. Matrix Anal. Appl., 12 (1991), 310320.Google Scholar
[Kus16] Kushel, V. Y., On the positive stability of P2 -matrices, Linear Algebra Appl., 503(2016), 190214.Google Scholar
[Lan90] Langer, H., Strictly copositive matrices and ESS’s, Arch. Math. (Basel), 55 (1990), 516520.Google Scholar
[Las14] Lasserre, J. B., New approximations for the cone of copositive matrices and its dual, Math. Program. Ser. A, 144 (2014), 265276.Google Scholar
[Lew80] Lewin, M., Totally nonnegative, M-, and Jacobi matrices, SIAM J. Alg. Disc. Meth., 1 (1980), 419421.Google Scholar
[Lew89] Lewin, M., On inverse M-matrices, Linear Algebra Appl., 118 (1989), 8394.Google Scholar
[LN80] Lewin, M. and Neumann, M., On the inverse M-matrix problem for (0, 1)-matrices, Linear Algebra Appl., 30 (1980), 4150.Google Scholar
[LLHNT98] Li, B., Li, L., Harada, M., Niki, H., and Tsatsomeros, M., An iterative criterion for H-matrices, Linear Algebra Appl., 271 (1998), 179190.Google Scholar
[LCW09] Li, Y. T., Chen, F. B., and Wang, D. F., New lower bounds on eigenvalue of the Hadamard product of an M-matrix and its inverse, Linear Algebra Appl., 430 (2009), 14231431.Google Scholar
[Loe89] Loewy, R., Linear transformations which preserve or decrease rank, Linear Algebra Appl., 121 (1989), 151161.Google Scholar
[Man69] Mangasarian, O. L., Nonlinear Programming, Corrected reprint of the 1969 original, Classics in Applied Mathematics, 10, Philadelphia: SIAM, 1994.Google Scholar
[Man78] Mangasarian, O. L., Characterization of linear complementarity problems as linear problems. Mathematical Programming Study, 7 (1978), 7487.Google Scholar
[MM59] Marcus, M. and Moyls, B. N., Linear transformations on algebras of matrices, Canadian J. Math, 11 (1959), 6166.Google Scholar
[Mark72] Markham, T. L., Nonnegative matrices whose inverses are M-matrices, Proc. Amer. Math. Soc., 36 (1972), 326330.Google Scholar
[Mark79] Markham, T. L., Two properties of M-matrices, Linear Algebra Appl., 28 (1979), 131134.Google Scholar
[MS98] Markham, T. L. and Smith, R. L., A Schur complement inequality for certain P-matrices, Linear Algebra Appl., 281 (1998), 3341.Google Scholar
[MJ81] Martin, D. H. and Jacobson, D. H., Copositive matrices and definiteness of quadratic forms subject to homogeneous linear inequality constraints, Linear Algebra Appl., 35 (1981), 227258.CrossRefGoogle Scholar
[MMS94] Martínez, S., Michon, G., and San Martín, J., Inverses of strictly ultrametric matrices are of Stieltjes type, SIAM J. Matrix Anal. Appl., 15 (1994), 98106.Google Scholar
[MSZ03] Martínez, S., San Martín, J., and Zhang, X.-D., A new class of inverse M-matrices of tree-like type, SIAM J. Matrix Anal. Appl., 24 (2003), 11361148.Google Scholar
[MH06] Mathews, J. H. and Howell, R. W., Complex Analysis for Mathematics and Engineering, 5th edition, Sudbury, MA: Jones and Bartlett, 2006.Google Scholar
[MP90] Mathias, R. and Pang, J.-S., Error bounds for the linear complementarity problem with a P-matrix, Linear Algebra Appl., 132 (1990), 123136.Google Scholar
[MNST95] McDonald, J. J., Neumann, M., Schneider, H., and Tsatsomeros, M. J., Inverse M-matrix inequalities and generalized ultrametric matrices, Linear Algebra Appl., 220 (1995), 321341.Google Scholar
[MNST96] McDonald, J. J., Neumann, M., Schneider, H., and Tsatsomeros, M. J., Inverses of unipathic M-matrices, SIAM J. of Matrix Anal. Appl., 17 (1996), 10251036.Google Scholar
[Meg88] Megiddo, N., A note on the complexity of P-matrix LCP and computing an equilibrium, Research report RJ 6439, 5 pages, San Jose, CA: IBM Almaden Research Center, 1988.Google Scholar
[MP91] Megiddo, N. and Papadimitriou, C. H., On total functions, existence theorems and computational complexity, Theoretical Computer Science, 81 (1991), 317324.Google Scholar
[MT09] Mendes-Araújo, C. and Torregrosa, J. R., Sign pattern matrices that admit M-, N-, P- or inverse M-matrices, Linear Algebra Appl., 431 (2009), 724731.Google Scholar
[Mey89a] Meyer, C. D., Uncoupling the Perron eigenvector problem, Linear Algebra Appl., 114/115 (1989), 6994.Google Scholar
[Mey89b] Meyer, C. D., Stochastic complementation, uncoupling Markov chains, and the theory of nearly reducible systems, SIAM Rev., 31 (1989), 240272.Google Scholar
[MND01] Mohan, S. R., Neogy, S. K., and Das, A. K., On the classes of fully copositive and fully semimonotone matrices, Linear Algebra Appl., 323 (2001), 8797.Google Scholar
[Mor03] Morris, W. D., Recognition of hidden positive row diagonally dominant matrices, Electron. J. Linear Algebra, 10 (2003), 102105.Google Scholar
[MN07] Morris, W. D. and Namiki, M., Good hidden P-matrix sandwiches, Linear Algebra Appl., 426 (2007), 325341.Google Scholar
[Mot52] Motzkin, T. S., Copositive quadratic forms, National Bureau of Standards, Report 1818 (1952), 1112.Google Scholar
[MS65] Motzkin, T. S. and Strauss, E. G., Maxima for graphs and a new proof of a theorem of Turán, Canad. J. Math., 17 (1965), 533540.Google Scholar
[Mur77] Murphy, B. B., On the inverses of M-matrices, Proc. Amer. Math. Soc., 62 (1977), 196198.Google Scholar
[MP98] Murthy, G. S. R., and Parthasarathy, T., Fully copositive matrices, Math. Programming Ser. A, 82 (1998), 401411.Google Scholar
[Mu71] Murty, K. G., On a characterization of P-matrices, SIAM J. Appl. Math., 20 (1971), 378384.Google Scholar
[MK87] Murty, K. G. and Kabadi, S. N., Some NP-complete problems in quadratic and nonlinear programming, Math. Programming, 39 (1987), 117129.Google Scholar
[Nab00] Nabben, R., A class of inverse M-matrices, Electron. J. Linear Algebra, 7 (2000), 5358.Google Scholar
[NV94] Nabben, R. and Varga, R. S., A linear algebra proof that the inverse of a strictly ultrametric matrix is a strictly diagonally dominant Stieltjes matrix, SIAM J. Matrix Anal. Appl., 15 (1994), 107113.Google Scholar
[NV95] Nabben, R. and Varga, R. S., Generalized ultrametric matrices – a class of inverse M-matrices, Linear Algebra Appl., 220 (1995), 365390.Google Scholar
[Neu98] Neumann, M., A conjecture concerning the Hadamard product of inverses of M-matrices, Linear Algebra Appl., 285 (1998), 277290.Google Scholar
[Neu00] Neumann, M., Inverses of Perron complements of inverse M-matrices, Linear Algebra Appl., 313 (2000), 163171.Google Scholar
[Neu98] Neumann, M., A conjecture concerning the Hadamard product of inverses of M-matrices, Linear Algebra Appl., 285 (1998), 277290.Google Scholar
[NP79] Neumann, M. and Plemmons, R., Generalized inverse-positivity and splittings of M-matrices, Linear Algebra Appl., 23 (1979), 2135.Google Scholar
[NP80] Neumann, M. and Plemmons, R., M-matrix characterizations II: General M-matrices, Linear Multilinear Algebra, 9 (1980), 211225.Google Scholar
[NS11] Neumann, M. and Sze, N.-S., On the inverse mean first passage matrix problem and the inverse M-matrix problem, Linear Algebra Appl., 434 (2011), 16201630.Google Scholar
[Ober] Nonnegative matrices, M-matrices and their generalizations, Oberwolfach, November 26–December 2, 2000. D. Hershkowitz, V. Mehrmann, and H. Schneider, organizers.Google Scholar
[Pan79a] Pang, J.-S., Hidden Z-matrices with positive principal minors, Linear Algebra Appl., 23 (1979), 201215.Google Scholar
[Pan79b] Pang, J.-S., On discovering hidden Z-matrices, In C. V. Coffman and G. Fix, editors, Constructive Approaches to Mathematical Models, pp. 231–241, Academic Press, 1979.Google Scholar
[Parth83] Parthasarathy, T., On Global Univalence Theorems, Lecture Notes in Math., Vol. 977, New York: Springer-Verlag, 1983.Google Scholar
[Parth96] Parthasarathy, T., Application of P matrices to economics, Applied Abstract Algebra, pp. 78–95, Delhi: University of Delhi, 1996.Google Scholar
[Pen95] Peña, J. M., M-matrices whose inverses are totally positive, Linear Algebra Appl., 221 (1995), 189193.Google Scholar
[Pen01] Peña, J. M., A class of P-matrices with applications to the localization of the eigenvalues of a real matrix, SIAM J. Matrix Anal. Appl., 22 (2001), 10271037.Google Scholar
[Pier92] Pierce, S. (Ed.), A survey of linear preserver problems, Linear Multilinear Algebra, 33 (1992), 1–129.Google Scholar
[PF93] Ping, L. and Feng, Y. Y., Criteria for copositive matrices of order four, Linear Algebra Appl., 194 (1993), 109124.Google Scholar
[Ple77] Plemmons, R. J., M-matrix characterizations. I – Nonsingular M-matrices, Linear Algebra Appl., 18 (1977), 175–188.Google Scholar
[Pok] Pokora, P., Introduction to Linear Preserver Problems, unpublished remarks.Google Scholar
[PB74] Poole, G. and Boullion, T., A survey on M-matrices, SIAM Rev., 16 (1974), 419427.Google Scholar
[Rock97] Rockafellar, R. T., Convex Analysis, Princeton, NJ: Princeton University Press, 1997.Google Scholar
[Roh87] Rohn, J., Inverse-positive interval matrices, Z. Angew. Math. Mech., 67 (1987) no. 5, T492–T493.Google Scholar
[Roh89] Rohn, J., Systems of linear interval equations, Linear Algebra Appl., 126 (1989), 3978.Google Scholar
[Roh91] Rohn, J., A theorem on P-matrices, Linear Multilinear Algebra, 30 (1991), 209211.Google Scholar
[RR96] Rohn, J. and Rex, G., Interval P-matrices, SIAM J. Matrix Anal. Appl., 17 (1996), 10201024.Google Scholar
[Rum01] Rump, S., Self-validating methods, Linear Algebra Appl., 324 (2001), 313.Google Scholar
[Rum03] Rump, S., On P-matrices, Linear Algebra Appl., 363 (2003), 237250.Google Scholar
[Rus07] Rüst, L. Y., The P-Matrix Linear Complementarity Problem – Generalizations and Specializations, Doctor of Sciences Dissertation, Swiss Federal Institute of Technology, Zurich, 2007.Google Scholar
[Schn65] Schneider, H., Positive Operators and an Inertia Theorem, Numerische Mathematik, 7 (1965), 1117.Google Scholar
[S-MBBJS15] Shaked-Monderer, N., Berman, A., Bomze, I. M., Jarre, F., and Schachinger, W., New results on the cp-rank and related properties of co(mpletely) positive matrices, Linear Multilinear Algebra, 63 (2015), no. 2, 384396.Google Scholar
[ST18] Sivakumar, K. C. and Tsatsomeros, M. J., Semipositive matrices and their semipositive cones, Positivity, 22 (2018), 379398.Google Scholar
[Smi81] Smith, R. L., M-matrices whose inverses are stochastic, SIAM J. Algebraic Discrete Methods, 2 (1981), 259265.Google Scholar
[Smi86] Smith, R. L., On the spectrum of N0 -matrices, Linear Algebra Appl., 83 (1986), 129134.Google Scholar
[Smi87] Smith, R. L., On Markham’s M-matrix properties, Linear Algebra Appl., 87 (1987), 189195.Google Scholar
[Smi88] Smith, R. L., Some notes on Z-matrices, Linear Algebra Appl., 106 (1988), 219231.Google Scholar
[Smi90] Smith, R. L., Bounds on the spectrum of nonnegative matrices and certain Z-matrices, Linear Algebra Appl., 129 (1990), 1328.Google Scholar
[Smi94] Smith, R. L., On Fan products of Z-matrices, Linear Multilinear Algebra, 37 (1994), 297302.Google Scholar
[Smi95] Smith, R. L., Some results on a partition of Z-matrices, Linear Algebra Appl., 223/224 (1995), 619629.Google Scholar
[Smi01] Smith, R. L., On characterizing Z-matrices, Linear Algebra Appl., 338 (2001), 99104.Google Scholar
[SH98] Smith, R. L. and Hu, S. A., Inequalities for monotonic pairs of Z-matrices, Linear Multilinear Algebra, 44 (1998), 5765.Google Scholar
[Son00] Song, Y. Z., On an inequality for the Hadamard product of an M-matrix and its inverse, Linear Algebra Appl., 305 (2000), 99105.Google Scholar
[SGR99] Song, Y., Gowda, M. S., and Ravindran, G., On some properties of P-matrix sets, Linear Algebra Appl., 290 (1999), 237246.Google Scholar
[Sou83] Soules, G. W., Constructing nonnegative symmetric matrices, Linear Multilinear Algebra, 13 (1983), 241151.Google Scholar
[Sou12] Souplet, P., Liouville-type theorems for elliptic Schrödinger systems associated with copositive matrices, Netw. Heterog. Media, 7 (2012), 967988.Google Scholar
[SRPM82] Stadelmaier, M., Rose, N., Poole, G., and Meyer, C., Nonnegative matrices with power invariant zero patterns, Linear Algebra Appl., 42 (1982), 2329.Google Scholar
[Stu98] Stuart, J. L., A polynomial time spectral decomposition test for certain classes of inverse M-matrices, Electron. J. Linear Algebra, 3 (1998), 129141.Google Scholar
[Szu90] Szulc, T., A contribution to the theory of P-matrices, Linear Algebra Appl., 139 (1990), 217224.Google Scholar
[TSOA07] Tang, A. K., Simsek, A., Ozdaglar, A., and Acemoglu, D., On the stability of P-matrices, Linear Algebra Appl., 426 (2007), 2232.Google Scholar
[TG05] Tao, J. and Gowda, M. S., Some P-properties for nonlinear transformations on Euclidean Jordan algebras, Mathematics of Operations Research, 30 (2005), 9851004.Google Scholar
[Tau58] Taussky, O., Research Problem #124, Bull. Amer. Math. Soc., 64 (1958).Google Scholar
[TV99] Todd, J. and Varga, R. S., Hardy’s inequality and ultrametric matrices, Linear Algebra Appl., 302/303 (1999), 3343.Google Scholar
[TT18] Torres, P. and Tsatsomeros, M., Stability and convex hulls of matrix powers, Linear Multilinear Algebra, 66 (2018), 769775.Google Scholar
[Tsa00] Tsatsomeros, M., Principal pivot transforms: properties and applications, Linear Algebra Appl., 307 (2000), 151165.Google Scholar
[TL00] Tsatsomeros, M. and Li, L., A recursive test for P-matrices, BIT, 40 (2000), 410414.Google Scholar
[Tsa16] Tsatsomeros, M., Geometric mapping properties of semipositive matrices, Linear Algebra Appl., 498 (2016), 349359.Google Scholar
[TW19] Tsatsomeros, M. and Wendler, M., Semimonotone matrices, Linear Algebra Appl., 578 (2019), 207224.Google Scholar
[TZ19] Tsatsomeros, M. and Zhang, Y. F.. The fiber of P-matrices: the recursive construction of all matrices with positive principal minors. Linear and Multilinear Algebra, submitted, 2019.Google Scholar
[Val86] Väliaho, H., Criteria for copositive matrices, Linear Algebra Appl., 81 (1986), 1934.Google Scholar
[Val88] Väliaho, H., Testing the definiteness of matrices on polyhedral cones, Linear Algebra Appl., 101 (1988), 135165.Google Scholar
[Val89a] Väliaho, H., Almost copositive matrices, Linear Algebra Appl., 116 (1989), 121134.Google Scholar
[Val89b] Väliaho, H., Quadratic-programming criteria for copositive matrices, Linear Algebra Appl., 119 (1989), 163182.Google Scholar
[Val91] Väliaho, H., A polynomial-time test for M-matrices, Linear Algebra Appl., 153 (1991), 183192.Google Scholar
[Van72] Vandergraft, J. S., Applications of partial orderings to the study of positive definiteness, monotonicity, and convergence of iterative methods for linear systems, SIAM J. Numer. Anal., 9 (1972), 97104.Google Scholar
[Vil1938] Ville, J., Sur a theorie generale des jeux ou intervient Vhabilite des joueurs, Traite du calcul des probability et de ses applications IV, 2 (1938), 105113.Google Scholar
[WZZ00] Wang, B. Y., Zhang, X., and Zhang, F., On the Hadamard product of inverse M-matrices, Linear Algebra Appl., 305 (2000), 2331.Google Scholar
[Wer94] Werner, H. J., Characterizations of minimal semipositivity, Linear Multilinear Algebra, 37 (1994), 273278.Google Scholar
[Wil77] Willoughby, R. A., The inverse M-matrix problem, Linear Algebra Appl., 18 (1977), 7594.Google Scholar
[XZ02] Xiu, N. and Zhang, J., A characteristic quantity of P-matrices, Appl. Math. Lett., 15 (2002), 4146.Google Scholar
[XY11] Xu, J. and Yao, Y., An algorithm for determining copositive matrices, Linear Algebra Appl., 435 (2011), 27842792.Google Scholar
[YX04] Yang, C. and Xu, C., Properties of Hadamard product of inverse M-matrices, Numer. Linear Algebra Appl., 11 (2004), 343354.Google Scholar
[YL09] Yang, S. and Li, X., Algorithms for determining the copositivity of a given symmetric matrix, Linear Algebra Appl., 430 (2009), no. 2–3, 609618.Google Scholar
[Yon00] Yong, X., Proof of a conjecture of Fiedler and Markham, Linear Algebra Appl., 320 (2000), 167171.Google Scholar
[YW99] Yong, X. and Wang, Z., On a conjecture of Fiedler and Markham, Linear Algebra Appl., 288 (1999), 259267.Google Scholar
[Zha05] Zhang, F. (Ed.), The Schur Complement and Its Applications, NewYork: Springer, 2005.Google Scholar
[ZZL11] Zhu, Y., Zhang, C. Y., and Liu, J., Path product and inverse M-matrices, Electron. J. Linear Algebra, 22 (2011), 644652.Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×