JP Journal of Algebra, Number Theory and Applications
Volume 5, Issue 1, Pages 163 - 172
(April 2005)
|
|
THE SOLVABILITY CONDITIONS FOR THE INVERSE PROBLEM OF SYMMETRIZABLE NONNEGATIVE DEFINITE MATRICES
Jin-Jun Hou (P. R. China), Zhen-Yun Peng (P. R. China) and Xu-Li Han (P. R. China)
|
Abstract: In this paper, we first consider the inverse problem as follows: Given two matrices X and B, find a matrix A such that AX = B, where A is a symmetrizable nonnegative definite matrix. The sufficient and necessary conditions are obtained, and a general representation of such a matrix is presented. We denote the set of such matrices by SE. Then the approximation problem for the inverse problem is discussed. That is: Given an arbitrary A*, find a matrix which is nearest to A* in the Frobenius norm. We show that the best approximation is unique and provide an expression for this nearest matrix. |
Keywords and phrases: symmetrizable nonnegative definite matrices, inverse problem, matrix nearness problem, matrix norm. |
|
Number of Downloads: 481 | Number of Views: 1175 |
|