Hostname: page-component-76fb5796d-skm99 Total loading time: 0 Render date: 2024-04-27T23:04:04.428Z Has data issue: false hasContentIssue false
  • English
  • Français

On Linear Matrix Equations

Published online by Cambridge University Press:  20 November 2018

P. Scobey  and
D.G. Kabe
P. Scobey
Affiliation:
Department of Mathematics St. Mary's University, Halifax, N.S., B3H 3C3
D.G. Kabe
Affiliation:
Department of Mathematics St. Mary's University, Halifax, N.S., B3H 3C3
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Some results from the theory of minimization of vector quadratic forms (subjected to linear restrictions) are used to obtain particular solutions to the usual types of linear matrix equations. An answer to a question raised by Greville [1] is supplied.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 23 , Issue 1 , 01 March 1980 , pp. 43 - 49
Copyright
Copyright © Canadian Mathematical Society 1980

References

1. Greville, T. N. E., Solution of the matrix equation XAX = X and relations between oblique and orthogonal projectors, SIAM J. Appl. Math., 26 (1974), 828-834.Google Scholar
2. Kabe, D. G., Minima of vector quadratic forms with applications to statistics, Metrika 12 (1968), 155-160.Google Scholar
3. Khatri, C. G. and Mitra, S. K., Hermitian and nonnegative definite solutions of linear matrix equations, SIAM J. Appl. Math., 31 (1976), 579-585.Google Scholar
4. Mitra, S. K., Fixed rank solutions to linear matrix equations, Sankhya Ser. A, 35 (1972), 387-392.Google Scholar
5. Mitra, S. K., Common solutions to a pair of matrix equations, A1XB1 = Cx, A2XB2= C2, Proc. Cambridge Phil. Soc, 74, (1973), 213-216.Google Scholar
6. Mitra, S. K., The matrix equation AXB + CXD = E, SIAM J. Appl. Math. 32 (1977), 823-825.Google Scholar
7. Rao, C. R., Estimation of variance and covariance components in linear models, J. Amer, Statisti. Assoc., 67 (1972), 112-115.Google Scholar