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Eigenvalues of matrix-valued analytic maps

Part of: General theory of linear operators

Published online by Cambridge University Press:  09 April 2009

K. R. Parthasarathy
K. R. Parthasarathy
Affiliation:
Indian Statistical Institute 7 S.J.S. Sansanwal Marg New Delhi, 110 029 India
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Abstract

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An elementary and self-contained account of analytic Jordan decomposition of matrix-valued analytic functions is given. An integral representation for their eigenvalues is obtained. This leads to estimates of the differences in eigenvalues and the number of points of degeneracy.

MSC classification

Secondary: 47A55: Perturbation theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 26 , Issue 2 , September 1978 , pp. 179 - 197
Copyright
Copyright © Australian Mathematical Society 1978

References

Kato, T. (1976), Perturbation Theory for Linear Operators, 2nd ed. (Springer-Verlag, New York).Google Scholar
Knopp, K. (1945), Theory of Functions, Part One (Dover, New York).Google Scholar
Uspensky, J. V. (1948), Theory of Equations (Tata McGraw-Hill, Bombay).Google Scholar