Diagonal and Monomial Solutions of the Matrix Equation AXB=C

Author(s):

Massoud Aman

Message:
Abstract:
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 explicit expressions of the optimal solution and the minimum norm solution are both provided.
Keywords:

Matrix equation , Diagonal matrix , Monomial matrix , Least squares problem

Language:
English
Published:
Iranian Journal of Mathematical Sciences and Informatics, Volume:9 Issue: 1, may 2014
Pages:
31 to 42
https://www.magiran.com/p1264170