The minimal rank of matrix expressions with respect to Hermitian matrix-revised. Issue 5 (March 2016) - Wang, Hongxing; Guo, Wenbin
Abstract: 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 ⁎ .