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

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.