The φS polar decomposition when the cosquare of S is normal

• 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
• Institution: De La Salle University

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...