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Paper Information

Journal:   IRANIAN JOURNAL OF MATHEMATICAL SCIENCES AND INFORMATICS (IJMSI)   2014 , Volume 9 , Number 1; Page(s) 31 To 42.
 
Paper: 

DIAGONAL AND MONOMIAL SOLUTIONS OF THE MATRIX EQUATION AX B=C

 
 
Author(s):  AMAN MASSOUD*
 
* DEPARTMENT OF MATHEMATICS, FACULTY OF SCIENCES, BIRJAND UNIVERSITY, BIRJAND, IRAN
 
Abstract: 

In this article, we consider the matrix equation AX B=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 -AX B F where X is a diagonal or monomial matrix. The explicit expressions of the optimal solution and the minimum norm solution are both provided.

 
Keyword(s): MATRIX EQUATION, DIAGONAL MATRIX, MONOMIAL MATRIX, LEAST SQUARES PROBLEM
 
References: 
 
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