Cayley transform and the Kronecker product of Hermitian matrices

TL;DR

This paper investigates when the Cayley transform of a Kronecker product of Hermitian matrices can itself be expressed as a Kronecker product, and explores related properties of the transform.

Contribution

It provides new conditions characterizing when the Cayley transform preserves the Kronecker product structure for Hermitian matrices.

Findings

Identifies conditions for the Cayley transform of a Kronecker product to be a Kronecker product.

Characterizes when the Cayley transform of matrices yields the Kronecker product of their transforms.

Provides insights into the structure-preserving properties of the Cayley transform.

Abstract

We consider the conditions under which the Cayley transform of the Kronecker product of two Hermitian matrices can be again presented as a Kronecker product of two matrices and, if so, if it is a product of the Cayley transforms of the two Hermitian matrices. We also study the related question: given two matrices, which matrix under the Cayley transform yields the Kronecker product of their Cayley transforms.