The sum of two φS orthogonal matrices when S−TS is normal and −1 ∈/ σ(S−TS)

The sum of two φS orthogonal matrices when S−TS is normal and −1 ∈/ σ(S−TS)

Let a nonsingular S ∈ Mn (C) be given. For A ∈ Mn (C), set φS (A) = S−1AT S. We say that A is φS symmetric if φS (A) = A; we say that A is φS orthogonal if A ∈ GLn and φS (A) = A−1; we say that A has a φS polar decomposition if A = UP for some φS orthogonal U and φS symmetric P. Suppose that S−T S i...

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Main Author: Granario, Daryl Q.
Format: text
Published: Animo Repository 2016
Subjects:
Orthogonal decompositions
Decomposition (Mathematics)
Mathematics
Online Access:https://animorepository.dlsu.edu.ph/faculty_research/11360
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Institution: De La Salle University
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spelling oai:animorepository.dlsu.edu.ph:faculty_research-133472023-12-02T00:49:00Z The sum of two φS orthogonal matrices when S−TS is normal and −1 ∈/ σ(S−TS) Granario, Daryl Q. Let a nonsingular S ∈ Mn (C) be given. For A ∈ Mn (C), set φS (A) = S−1AT S. We say that A is φS symmetric if φS (A) = A; we say that A is φS orthogonal if A ∈ GLn and φS (A) = A−1; we say that A has a φS polar decomposition if A = UP for some φS orthogonal U and φS symmetric P. Suppose that S−T S is normal and −1 ∈/ σ S−T S. We determine conditions on A ∈ Mn (C) so that A can be written as a sum of two φS orthogonal matrices. 2016-01-01T08:00:00Z text https://animorepository.dlsu.edu.ph/faculty_research/11360 Faculty Research Work Animo Repository Orthogonal decompositions Decomposition (Mathematics) 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 Orthogonal decompositions
Decomposition (Mathematics)
Mathematics
spellingShingle Orthogonal decompositions
Decomposition (Mathematics)
Mathematics
Granario, Daryl Q.
The sum of two φS orthogonal matrices when S−TS is normal and −1 ∈/ σ(S−TS)
description Let a nonsingular S ∈ Mn (C) be given. For A ∈ Mn (C), set φS (A) = S−1AT S. We say that A is φS symmetric if φS (A) = A; we say that A is φS orthogonal if A ∈ GLn and φS (A) = A−1; we say that A has a φS polar decomposition if A = UP for some φS orthogonal U and φS symmetric P. Suppose that S−T S is normal and −1 ∈/ σ S−T S. We determine conditions on A ∈ Mn (C) so that A can be written as a sum of two φS orthogonal matrices.
format text
author Granario, Daryl Q.
author_facet Granario, Daryl Q.
author_sort Granario, Daryl Q.
title The sum of two φS orthogonal matrices when S−TS is normal and −1 ∈/ σ(S−TS)
title_short The sum of two φS orthogonal matrices when S−TS is normal and −1 ∈/ σ(S−TS)
title_full The sum of two φS orthogonal matrices when S−TS is normal and −1 ∈/ σ(S−TS)
title_fullStr The sum of two φS orthogonal matrices when S−TS is normal and −1 ∈/ σ(S−TS)
title_full_unstemmed The sum of two φS orthogonal matrices when S−TS is normal and −1 ∈/ σ(S−TS)
title_sort sum of two φs orthogonal matrices when s−ts is normal and −1 ∈/ σ(s−ts)
publisher Animo Repository
publishDate 2016
url https://animorepository.dlsu.edu.ph/faculty_research/11360
_version_ 1784863535478603776

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