The φS polar decomposition when the cosquare of S is normal

The φS polar decomposition when the cosquare of S is normal

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...

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Main Authors: Granario, Daryl Q., Merino, Dennis I., Paras, Agnes T.
Format: text
Published: Animo Repository 2015
Subjects:
Decomposition (Mathematics)
Symmetric matrices
Mathematics
Online Access:https://animorepository.dlsu.edu.ph/faculty_research/11362
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Institution: De La Salle University
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spelling oai:animorepository.dlsu.edu.ph:faculty_research-133452023-12-02T00:08:18Z The φS polar decomposition when the cosquare of S is normal Granario, Daryl Q. Merino, Dennis I. Paras, Agnes T. 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). 2015-01-01T08:00:00Z text https://animorepository.dlsu.edu.ph/faculty_research/11362 Faculty Research Work Animo Repository Decomposition (Mathematics) Symmetric matrices Mathematics
institution De La Salle University
building De La Salle University Library
continent Asia
country Philippines
Philippines
content_provider De La Salle University Library
collection DLSU Institutional Repository
topic Decomposition (Mathematics)
Symmetric matrices
Mathematics
spellingShingle Decomposition (Mathematics)
Symmetric matrices
Mathematics
Granario, Daryl Q.
Merino, Dennis I.
Paras, Agnes T.
The φS polar decomposition when the cosquare of S is normal
description 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).
format text
author Granario, Daryl Q.
Merino, Dennis I.
Paras, Agnes T.
author_facet Granario, Daryl Q.
Merino, Dennis I.
Paras, Agnes T.
author_sort Granario, Daryl Q.
title The φS polar decomposition when the cosquare of S is normal
title_short The φS polar decomposition when the cosquare of S is normal
title_full The φS polar decomposition when the cosquare of S is normal
title_fullStr The φS polar decomposition when the cosquare of S is normal
title_full_unstemmed The φS polar decomposition when the cosquare of S is normal
title_sort φs polar decomposition when the cosquare of s is normal
publisher Animo Repository
publishDate 2015
url https://animorepository.dlsu.edu.ph/faculty_research/11362
_version_ 1784863534526496768

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