# Some investigation on Hermitian positive definite solutions of the matrix equation [formula omitted]

- Authors
- Journal
- Linear Algebra and its Applications 0024-3795
- Publisher
- Elsevier
- Publication Date
- Volume
- 430
- Identifiers
- DOI: 10.1016/j.laa.2008.12.033
- Keywords

## Abstract

Abstract In this paper, the Hermitian positive definite solutions of the matrix equation X s + A ∗ X - t A = Q are considered, where Q is an Hermitian positive definite matrix, s and t are positive integers. Necessary and sufficient conditions for the existence of an Hermitian positive definite solution are derived. A sufficient condition for the equation to have only two different Hermitian positive definite solutions and the formulas for these solutions are obtained. In particular, the equation with the case AQ 1 2 = Q 1 2 A is discussed. A necessary condition for the existence of an Hermitian positive definite solution and some new properties of the Hermitian positive definite solutions are given, which generalize the existing related results.

## There are no comments yet on this publication. Be the first to share your thoughts.