The minimal rank of matrix expressions with respect to Hermitian matrix-revised

This paper presents representations for the minimal rank of A−BXC with respect to Hermitian matrix X and the minimal rank of A−BX−YD with respect to Hermitian matrix X and Y. These results prove, in a distinctive way, the solvability conditions of the matrix equations BXC=A and BX+YD=A, where X and Y are arbitrary matrices with X=X⁎.