Hostname: page-component-8448b6f56d-42gr6 Total loading time: 0 Render date: 2024-04-23T07:38:15.043Z Has data issue: false hasContentIssue false
  • English
  • Français

When is a Matrix Sign Stable?

Published online by Cambridge University Press:  20 November 2018

Clark Jeffries ,
Victor Klee  and
Pauline Van Den Driessche
Clark Jeffries
Affiliation:
University of Regina, Regina, Saskatchewan
Victor Klee
Affiliation:
University of Washington, Seattle, Washington
Pauline Van Den Driessche
Affiliation:
University of Victoria, Victoria, British Columbia
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.

An n X n real matrix A = (aij) is called stable (resp. semistable) if each of its eigenvalues has negative (resp. nonpositive) real part. These notions are important because of their close connection with the stability of motion, which can be described especially simply for a system

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 29 , Issue 2 , 01 April 1977 , pp. 315 - 326
Copyright
Copyright © Canadian Mathematical Society 1977

References

1. Anderson, W. M., Maximum matchings and the rank of a matrix, SIAM J. Appl. Math. 28 (1975), 114–123.Google Scholar
2. Cesari, L., Asymptotic behavior and stability problems in ordinary differential equations (Springer-Verlag, New York-Heidelberg-Berlin, 1971).Google Scholar
3. Clarke, B. L., Theorems on chemical network stability, J. Chem. Phys. 62 (1975), 773–775.Google Scholar
4. Coddington, E. and Levinson, N., Theory of ordinary differential equations (McGraw-Hill, New York, 1955).Google Scholar
5. Hahn, W., Stability of motion (Springer-Verlag, Berlin-Heidelberg-New York, 1967).Google Scholar
6. Jeffries, C., Qualitative stability and digraphs in model ecosystems, Ecology 55 (1974), 1415–1419.Google Scholar
7. Klee, V. and P. van den Driessche, Linear algorithms for testing the sign stability of a matrix and for finding Z-maximum matchings in acyclic graphs, Numerische Math., to appear.Google Scholar
8. Levins, R., The qualitative analysis of partially specified systems, Ann. New York Acad. Sci. 231 (1974), 123–138.Google Scholar
9. Levins, R. Problems of signed digraphs in ecological theory, in Ecosystem Analysis and Prediction (S. Levin, éd.), 1974, 264–277.Google Scholar
10. May, R. M., Qualitative stability in model ecosystems, Ecology 54 (1973), 638–641.Google Scholar
11. May, R. M. Stability and complexity in model ecosystems (Princeton Univ. Press, 1973).Google Scholar
12. Maybee, J. S., Combinatorially symmetric matrices, Linear Algebra and its Applications 8 (1974), 529–537.Google Scholar
13. Maybee, J. and j. Quirk, Qualitative problems in matrix theory, SIAM Review 11 (1969), 30–51.Google Scholar
14. Quirk, J. and Ruppert, R., Qualitative economics and the stability of equilibrium, Rev. Economic Studies 32 (1965), 311–326.Google Scholar
15. Samuelson, P. A., Foundations of economic analysis (Harvard Univ. Press, Cambridge, Mass., 1955).Google Scholar
16. Tyson, J., Classification of instabilities in chemical reaction systems, J. Chem. Phys. 62 (1975), 1010–1015.Google Scholar