Solutions of a second-order conjugate matrix equation
Yongxin Yuan, Yinlan Chen, Lei Zhou · Linear and Multilinear Algebra · 2019
The following second-order conjugate matrix equation is considered XHAX+BHX+XHB+D=0, where AH=A∈Cn×n,B∈Cn×p,DH=D∈Cp×p are known matrices and X∈Cn×p is an unknown matrix to be determined. The necessary and sufficient condition for the matrix equation to have a solution is established and the explicit solutions of the equation are provided.