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


    • Department of Applied MathematicsShanghai Finance University
  • Yongge Tian
    • China Economics and Management AcademyCentral University of Finance and Economics

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)

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© Korean Society for Computational and Applied Mathematics 2009