The skew-symmetric orthogonal solutions of the matrix equation AX=B

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...

On solutions to the quaternion matrix equation AXB+CYD=E

Expressions, as well as necessary and sufficient conditions are given for the existence of the real and pure imaginary solutions to the consistent quaternion matrix equation AXB+CY D = E. Formulas are established for the extreme ranks of real matrices Xi, Yi, i = 1, · · · , 4, in a solution pair X = X1 +X2i+X3j+X4k and Y = Y1+Y2i+Y3j+Y4k to this equation. Moreover, necessary and sufficient cond...

Iterative solutions to the linear matrix equation AXB + CXTD = E

In this paper the gradient based iterative algorithm is presented to solve the linear matrix equation AXB +CXD = E, where X is unknown matrix, A,B,C,D,E are the given constant matrices. It is proved that if the equation has a solution, then the unique minimum norm solution can be obtained by choosing a special kind of initial matrices. Two numerical examples show that the introduced iterative a...

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