Volume 9, Issue 1 (5-2014)                   IJMSI 2014, 9(1): 31-42 | Back to browse issues page

DOI: 10.7508/ijmsi.2014.01.003

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Aman M. Diagonal and Monomial Solutions of the Matrix Equation AXB=C. IJMSI. 2014; 9 (1) :31-42
URL: http://ijmsi.ir/article-1-300-en.html


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.

Type of Study: Research | Subject: Special

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