The least extremal solution of the operator equation AXB = C
نویسندگان
چکیده
منابع مشابه
A new Approximation to the solution of the linear matrix equation AXB = C
It is well-known that the matrix equations play a significant role in several applications in science and engineering. There are various approaches either direct methods or iterative methods to evaluate the solution of these equations. In this research article, the homotopy perturbation method (HPM) will employ to deduce the approximated solution of the linear matrix equation in the form AXB=C....
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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...
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2 A denote the transpose, Moore-Penrose generalized inverse, Frobenius norm and Euclid norm, respectively. For any , m n A B R , , 0 T A B trace B A denotes the inner product of A and B . Therefore, m n R is a complete inner product space endowed with 2 , A A A . For any non-zero matrices 1 2 , , , m n k A A A R , if , T j i i A A trace A 0 j A i j , then it is...
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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...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1990
ISSN: 0022-247X
DOI: 10.1016/0022-247x(90)90042-e