Sufficient conditions for the unique solution of a class of new Sylvester-like absolute value equation

TL;DR

This paper investigates a new class of Sylvester-like absolute value equations, providing sufficient conditions for the existence of a unique solution, thereby extending previous work in the field.

Contribution

It introduces new Sylvester-like AVEs and derives sufficient conditions for their unique solutions, which are distinct from prior research.

Findings

Derived sufficient conditions for unique solutions

Extended the theory of Sylvester-like AVEs

Compared with existing results in the literature

Abstract

In this paper, a class of new Sylvester-like absolute value equation (AVE) $AXB-|CXD|=E$ with $A,C\in \mathbb{R}^{m\times n}$, $B,D\in \mathbb{R}^{p\times q}$ and $E\in \mathbb{R}^{m\times q}$ is considered, which is quite distinct from the published work by Hashemi [Applied Mathematics Letters, 112 (2021) 106818]. Some sufficient conditions for the unique solution of the Sylvester-like AVE are obtained.