Affordable Access

Publisher Website

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
  • Matrix Equation
  • Hermitian Positive Definite Solution
  • Existence

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.

Statistics

Seen <100 times
0 Comments