The sum of two φS orthogonal matrices when S−TS is normal and −1 ∈/ σ(S−TS)
Added Title
The sum of two phi S orthogonal matrices when S−TS is normal and −1 ∈/ σ(S−TS)
College
College of Science
Department/Unit
Mathematics and Statistics Department
Document Type
Article
Source Title
Linear Algebra and its Applications
Volume
495
First Page
67
Last Page
89
Publication Date
2016
Abstract
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.
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Recommended Citation
Granario, D. Q. (2016). The sum of two φS orthogonal matrices when S−TS is normal and −1 ∈/ σ(S−TS). Linear Algebra and its Applications, 495, 67-89. Retrieved from https://animorepository.dlsu.edu.ph/faculty_research/11360
Disciplines
Mathematics
Keywords
Orthogonal decompositions; Decomposition (Mathematics)
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