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

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 A₁X₁A^*₁ = B₁{A_{1}X_{1}A^{*}_{1} = B_{1}} and A₂X₂A^*₂ = B₂{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.