A Class Of Inverse Problems Of Matrix Equation AX=B

First of all anti-matrix problems raised by the J.B.Keller,This caused greatinterest to scholars at home and abroad, and achieved rich results. Many studies have a wide range of applications in the economic, automatic control, vibration theory. Professor Dai Hua eigenvalues problem of anti-divided into the following issues: addition and multiplication problems, including parameters of the characteristics of anti-values issues, Jacobi matrix and is symmetrical with - Eigenvalue problem of anti-linear (spectrum) matrix under the restraints of the best approximation problem, pole placement and characteristics of anti-matrix generalized problem.In this paper, the following issues were discussedSecondly,let X, B∈C^n×m, CB⁺ + (CB⁺ )^H > 0 ,this paper considers the problem:find the positive definite matrix A∈C^n×n,such that AX = B.This paper gives thenecessary and sufficient condition for inverse problem of AX=B has positive define solution. Furthermore, the expression of general solutions are given.Let X , B∈R^n×m , S(?)R^n×n . Find AeS such that: AX = B .When S is allanti-symmetric matrices set, The paper proved the existence of solution for the problem.Again,let X,B∈R^n×m, This paper discusses the problem of anti-symmetricortho-symmetric matrices. i.e. the sufficient and necessary conditions for the solvability solutions to AX = B.Finally, the paper discusses some interrelated problem of perturbation analysis for matrices equation AX=B.