Hostname: page-component-7bb8b95d7b-wpx69 Total loading time: 0 Render date: 2024-09-16T21:02:53.397Z Has data issue: false hasContentIssue false

On Spectral Properties of Matrices with Positive Characteristic Vectors

Published online by Cambridge University Press:  20 November 2018

Kulendra N. Majindar*
Affiliation:
Loyola College, Montreal, P. Q.
Rights & Permissions [Opens in a new window]

Extract

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.

Unless stated otherwise, all our matrices (denoted by capital letters) are square matrices of size n × n and composed of real numbers. A' denotes the transpose of A. The characteristic or eigenvectors of matrices are written as column vectors having n coordinates. If ζ is a vector, ζ’ denotes its transpose.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1968

References

1. Brauer, A., On the characteristic roots of power-positive matrices, Duke Math. J. 28 (1961), 439445.Google Scholar
2. Brauer, A., on the characteristic roots of non-negative matrices {Recent advances in matrix theory, Proc. Advanced Seminar, Math. Res. Center, U.S. Army, Univ. Wisconsin, Madison, Wisconsin, 1963, pp. 338; (Univ. Wisconsin Press, Madison, Wisconsin, 1964).Google Scholar
3. Brauer, A., A method for the computation of the greatest root of a non-negative matrix, SI AM J. Numer. Anal. 3 (1966), 564569.Google Scholar
4. Gantmacher, F. R., The theory of matrices, Vol. II, pp. 5152 (Chelsea, New York, 1960).Google Scholar
5. Holladay, J. C. and Varga, R. S., On powers of non-negative matrices, Proc. Amer. Math. Soc. 9 (1958), 631634.Google Scholar