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

• 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
• Institution: De La Salle University

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...