The ψS polar decomposition when the cosquare of S is normal
- D. Q. Granario, D. I. Merino, A. T. Paras
- Linear Algebra Appl.,
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.