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


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


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.


Maximal rankMinimal rankSubmatricesHermitian solutionSkew-Hermitian solutionmatrix equation

Mathematics Subject Classification (2000)


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