ADMM-Based Methods for Nearness SkewSymmetric and Symmetric Solutions of Matrix Equation AXB = C

Diagonal and Monomial Solutions of the Matrix Equation AXB=C

In this article, we consider the matrix equation $AXB=C$, where A, B, C are given matrices and give new necessary and sufficient conditions for the existence of the diagonal solutions and monomial solutions to this equation. We also present a general form of such solutions. Moreover, we consider the least squares problem $min_X |C-AXB |_F$ where $X$ is a diagonal or monomial matrix. The explici...

Re-nnd solutions of the matrix equation AXB = C

In this article we consider Re-nnd solutions of the equation AXB = C with respect to X, where A,B, C are given matrices. We give necessary and sufficient conditions for the existence of Re-nnd solutions and present a general form of such solutions. As a special case when A = I we obtain the results from paper of J. Gross (Explicit solutions to the matrix inverse problem AX = B, Linear Algebra A...

Iterative Method for Mirror-Symmetric Solution of Matrix Equation AXB + CY D = E

Conjugate Gradient Algorithm for the Symmetric Arrowhead Solution of Matrix Equation AXB=C

2 A denote the transpose, Moore-Penrose generalized inverse, Frobenius norm and Euclid norm, respectively. For any , m n A B  R ,   , 0 T A B trace B A   denotes the inner product of A and B . Therefore, m n R  is a complete inner product space endowed with 2 , A A A  . For any non-zero matrices 1 2 , , , m n k A A A  R  , if  , T j i i A A trace A     0 j A i j   , then it is...

On the optimal approximation for the symmetric Procrustes problems of the matrix equation AXB = C

The explicit analytical expressions of the optimal approximation solutions for the symmetric Procrustes problems of the linear matrix equation AXB = C are derived, with the projection theorem in Hilbert space , the quotient singular value decomposition (QSVD) and the canonical correlation decomposition (CCD) being used.