The phiS polar decomposition when the cosquare of S is nonderogatory

  • Ralph John Lamadrid, Daryl Granario, IS NONDEROGATORY, RALPH JOHN DE LA CRUZ, DARYL Q. GRANARIO
  • Published 2017

Abstract

For S ∈ GLn, define φS : Mn → Mn by φS(A) = S AS. A matrix A ∈ Mn is φS orthogonal if φS(A) = A ; A is φS symmetric if φS(A) = A; A has a φS polar decomposition if A = ZY for some φS orthogonal Z and φS symmetric Y . If A has a φS polar decomposition, then A commutes with the cosquare SS. Conditions under which the converse implication holds for the case where SS is nonderogatory, are obtained.

Cite this paper

@inproceedings{Lamadrid2017ThePP, title={The phiS polar decomposition when the cosquare of S is nonderogatory}, author={Ralph John Lamadrid and Daryl Granario and IS NONDEROGATORY and RALPH JOHN DE LA CRUZ and DARYL Q. GRANARIO}, year={2017} }