Title :
The generalized reflexive solutions of the matrix equation AX = B
Author :
Liu, Zhibing ; Xu, Chengfeng ; Wang, Kanmin
Author_Institution :
Coll. of Sci., Jiujiang Univ., Jiujiang, China
Abstract :
In this paper, we consider the generalized reflexive solutions of the matrix equation AX = B. The necessary and sufficient conditions for the solvability of the problem are given, moreover, a simple and eigenvector-free formula of the general solution to the matrix equation is presented using Moore-Penrose generalized inverses of the coefficient matrix A. In addition, in corresponding solution set of the equation, the explicit expression of the nearest matrix to a given matrix in the Frobenius norm has been provided..
Keywords :
matrix algebra; Frobenius norm; Moore-Penrose generalized inverses; eigenvector free formula; generalized reflexive solutions; matrix coefficent; matrix equation AX = B; Approximation methods; Bismuth; Educational institutions; Electronic mail; Equations; Matrices; Generalized reflexive matrix; Matrix equation; Matrix nearness problem;
Conference_Titel :
Computer Science and Service System (CSSS), 2011 International Conference on
Conference_Location :
Nanjing
Print_ISBN :
978-1-4244-9762-1
DOI :
10.1109/CSSS.2011.5972240
