$A $, $ C$ (n$(n,n)$ are symmetric PSD matrices,n)$\;are \;symmetric\; PSD \; matrices, $B $B$ is PD symmetric matrix, and $H_i$ $\;is\;PD symmetric \;matrix ,and $$\; $ $H_i$$(i=[1,m])$ represent $\; $$(i=[1,m]) $$ represent $ m$ m $ complex matrices. $ complexe matrices. $$ H_i$$H_i$ are all one rank matrix
Our objectif is to find PSD matrix X that enable:
$A\sum\limits_{i = 1}^{m - 1} {{H_i}(B + X){H_i} + A(X + B) + {H_m}(B + X) = C}$