The φS polar decomposition when the cosquare of S is normal

Added Title

The phi S polar decomposition when the cosquare of S is normal

College

College of Science

Department/Unit

Mathematics and Statistics Department

Document Type

Article

Source Title

Linear Algebra and its Applications

Volume

467

First Page

75

Last Page

85

Publication Date

2015

Abstract

Let S ∈ Mn(C) be nonsingular such that S−T S is normal (that is, the cosquare of S is normal). Set φS(A) = S−1AT S for A ∈ Mn(C). We determine conditions on A so that A has a φS polar decomposition. We also find the possible Jordan Canonical Forms of a φS orthogonal matrix and of a φS skew symmetric matrix in the cases (a) 1 ∈/ σ(S−T S) and (b) −1 ∈/ σ(S−T S).

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Disciplines

Mathematics

Keywords

Decomposition (Mathematics); Symmetric matrices

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