Journal of Applied Mathematics and Computing

, Volume 32, Issue 2, pp 289–301

Extremal ranks of submatrices in an Hermitian solution to the matrix equation AXA*=B with applications

Article

DOI: 10.1007/s12190-009-0251-8

Cite this article as:
Liu, Y. & Tian, Y. J. Appl. Math. Comput. (2010) 32: 289. doi:10.1007/s12190-009-0251-8

Abstract

Suppose that AXA*=B is a consistent matrix equation and partition its Hermitian solution X*=X into a 2-by-2 block form. In this paper, we give some formulas for the maximal and minimal ranks of the submatrices in an Hermitian solution X to AXA*=B. From these formulas we derive necessary and sufficient conditions for the submatrices to be zero or to be unique, respectively. As applications, we give some properties of Hermitian generalized inverses for an Hermitian matrix.

Keywords

Maximal rank Minimal rank Submatrices Hermitian solution Skew-Hermitian solution matrix equation 

Mathematics Subject Classification (2000)

15A03 15A09 15A24 

Copyright information

© Korean Society for Computational and Applied Mathematics 2009

Authors and Affiliations

  1. 1.Department of Applied MathematicsShanghai Finance UniversityShanghaiPeople’s Republic of China
  2. 2.China Economics and Management AcademyCentral University of Finance and EconomicsBeijingPeople’s Republic of China

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