Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-27T02:17:24.234Z Has data issue: false hasContentIssue false
  • English
  • Français

Spectra of irreducible matrices

Published online by Cambridge University Press:  20 January 2009

Henryk Minc
Henryk Minc
Affiliation:
Institute for Algebra and Combinatorics, University of California, Santa Barbara, 93106, U.S.A.
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.

A real matrix is called non-negative (positive) if all its entries are non-negative (positive). Two matrices A and B are said to be cogredient if there exists a permutation matrix Q such that QAQT = B. A square non-negative matrix is called reducible if it is cogredient to a matrix of the form

where the blocks X and Y are square. Otherwise it is called irreducible.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 19 , Issue 3 , March 1975 , pp. 231 - 236
Copyright
Copyright © Edinburgh Mathematical Society 1975

References

REFERENCES

(1)Frobenius, G., Über Matrizen aus nicht negativen Elementen, S.-B. Deutsch. Akad. Wiss. Berlin Math.-Nat. Kl. (1912), 456–477.Google Scholar
(2)Gantmacher, F. R., The Theory of Matrices, vol. II (Chelsea Publishing Company, New York, 1959).Google Scholar
(3)Minc, H., Irreducible matrices, Linear and Multilinear Algebra 1 (1974), 337–342.CrossRefGoogle Scholar
(4)Minc, H., The structure of irreducible matrices, Linear and Multilinear Algebra 2(1974), 85–90.CrossRefGoogle Scholar
(5)Mirsky, L., An inequality for characteristic roots and singular values of complex matrices, Monatsh. Math. 70 (1966), 357–359.CrossRefGoogle Scholar
(6)Sylvester, J. J., On the equation to the secular inequalities in the planetary theory, Philos. Mag. (5) 16 (1883), 267–269.CrossRefGoogle Scholar