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Invariant Neutral Subspaces for Symmetric and Skew Real Matrix Pairs

Published online by Cambridge University Press:  20 November 2018

P. Lancaster  and
L. Rodman
P. Lancaster
Affiliation:
Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, T2N 1N4
L. Rodman
Affiliation:
Department of Mathematics, College of William and Mary, Williamsburg, Virginia 23187-8795, U.S.A.
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Abstract

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Real matrix pairs (A,H) satisfying det H ≠ 0, HT = εH, and HA - ηATH, where ε, η take the values +1 or —1, are considered. It is shown that maximal A-invariant H-neutral subspaces have the same dimension (depending on ε and η), called the order of neutrality of the pair (A, H). The order of neutrality of definitizable pairs is investigated. In particular, this concept is used to obtain lower bounds for the number of pure imaginary eigenvalues of low rank perturbations of definitizable pairs when (ε,η) = (1, - 1 ) and when (ε,η) = (—1,—1).

Keywords

15A2115A57indefinite scalar productsmatrix pairsdefinitizable pairsinvariant subspaces
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 46 , Issue 3 , 01 June 1994 , pp. 602 - 618
Copyright
Copyright © Canadian Mathematical Society 1994

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