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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| Format: | text |
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Animo Repository
2016
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| Online Access: | https://animorepository.dlsu.edu.ph/faculty_research/11360 |
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| Institution: | De La Salle University |
| Summary: | 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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