دوره 9، شماره 1 - ( 2-1393 )
جلد 9 شماره 1 صفحات 42-31 |
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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-fa.html
URL: http://ijmsi.ir/article-1-300-fa.html
امان مسعود. جوابهایی از نوع ماتریسهای قطری و تک جمله ای برای معادله ماتریسی AXB=C. مجله علوم ریاضی و انفورماتیک. 1393; 9 (1) :31-42
چکیده:
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.
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