Mediterranean Journal of Mathematics

, Volume 9, Issue 1, pp 47–60

# On Additive Decomposition of the Hermitian Solution of the Matrix Equation AXA* = B

Article

## Abstract

The decomposition of a Hermitian solution of the linear matrix equation AXA* = B into the sum of Hermitian solutions of other two linear matrix equations $${A_{1}X_{1}A^{*}_{1} = B_{1}}$$ and $${A_{2}X_{2}A^*_{2} = B_{2}}$$ are approached. As applications, the additive decomposition of Hermitian generalized inverse C = A + B for three Hermitian matrices A, B and C is also considered.

## Mathematics Subject Classification (2010)

15A03 15A09 15A24 15B57

## Keywords

Matrix equation Hermitian solution decomposition of solution set inclusion generalized inverse rank formulas for partitioned matrices

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