Journal of applied mathematics & informatics

한국전산응용수학회 (The Korean Society for Computational and Applied Mathematics)
권호 표지

THE GENERAL HERMITIAN NONNEGATIVE-DEFINITE AND POSITIVE-DEFINITE SOLUTIONS TO THE MATRIX EQUATION $GXG^*\;+\;HYH^*\;=\;C$

  • Zhang, Xian (Department of Mathematics, Heilongjiang Univ., School of Mechanical and Manufacturing Engineering, The Queen's University of Belfast)
  • 발행 : 2004.01.01

⟨ 이전 논문 다음 논문 ⟩

초록

A matrix pair $(X_0,\;Y_0)$ is called a Hermitian nonnegative-definite(respectively, positive-definite) solution to the matrix equation $GXG^*\;+\;HYH^*\;=\;C$ with unknown X and Y if $X_{0}$ and $Y_{0}$ are Hermitian nonnegative-definite (respectively, positive-definite) and satisfy $GX_0G^*\;+\;HY_0H^*\;=\;C$. Necessary and sufficient conditions for the existence of at least a Hermitian nonnegative-definite (respectively, positive-definite) solution to the matrix equation are investigated. A representation of the general Hermitian nonnegative-definite (respectively positive-definite) solution to the equation is also obtained when it has such solutions. Two presented examples show these advantages of the proposed approach.

키워드

참고문헌

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