Unitary equivalence to a complex symmetric matrix: a modulus criterion

TL;DR

This paper introduces a new procedure to determine if a square complex matrix is unitarily equivalent to a complex symmetric matrix, offering advantages over previous methods and supported by illustrative examples.

Contribution

The paper presents a novel modulus-based criterion for identifying unitary equivalence to complex symmetric matrices, improving upon existing techniques.

Findings

The new criterion effectively distinguishes complex symmetric matrices.

The approach simplifies the verification process compared to prior methods.

Numerical examples demonstrate the criterion's applicability and advantages.

Abstract

We develop a procedure for determining whether a square complex matrix is unitarily equivalent to a complex symmetric (i.e., self-transpose) matrix. Our approach has several advantages over existing methods. We discuss these differences and present a number of examples.