A note on the similarity of matrix and its conjugate transpose

John Walter Duke

Vol. 31 (1969), No. 2, 321–323

DOI: 10.2140/pjm.1969.31.321

Abstract

It is well-known that each square matrix A over a field is similar to its transpose A^T and there exists a nonsingular symmetric matrix P for which PA^T = AP. The purpose of this note is to show that if A is similar to its conjugate transpose A^∗ then, under certain conditions, there exists a nonsingular Hermitian matrix Q for which QA^∗ = AQ.

Mathematical Subject Classification

Primary: 15.30

Milestones

Received: 3 January 1969

Published: 1 November 1969