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Generalized normal matrices. (English) Zbl 1174.15013

Summary: A matrix \(A \in M_n(C)\) is called generalized normal provided that there is a positive definite Hermite matrix \(H\) such that \(HAH\) is normal. In this paper, these matrices are investigated and their canonical form, invariants and relative properties in the sense of congruence are obtained.

MSC:

15B57 Hermitian, skew-Hermitian, and related matrices
15A21 Canonical forms, reductions, classification
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References:

[1] Horn R A, Johnson C R. Matrix Analysis, Cambridge: Cambridge University Press, 1985, 79–482. · Zbl 0576.15001
[2] Beckenbach E F, Bellman R. Inequalities, Berlin: Springer, 1983, 26–26.
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