关于实方阵的几个问题

本文讨论如下内容：１．把有关对称正定（半正定）的一些性质推广到广义正定（半正定）。２．给定ｘ∈Ｒｍ×ｍ，∧为对角阵，求ＡＸ＝ｘ∧在对称半正定矩阵类中解存在的充要条件及一般形式，并讨论了对任意给定的对称正定（半正定）矩阵Ａ，在上述解的集合中求得Ａ，使得

Some Problems About the Real Square Matrices

In this paper, three things are discussed:1. Some qualities about Symmetric Positive Definite (positive semidefinite matrix) are extended to Generalized positive definite (positive semidefinite matrix). 2. The essential and full condition and the general form of solution to the equation AX=X ∧ in the Symmetic positive semidefinite matrix, matrix class are presented in this equation, X∈Rn×m, ∧ is a diagonal Matrix, and the method getting A (ensuring || A-A ||,r=inf|| A-A ||f) form the above solution set on the situation of the given Symmetricpositive definite (positive semidefinite mauix) Matrix A at will is discussed.3. Present a theorem to determine the half metra positive definite properties of matrices of high order by the symmetric half positive definine propetites of low arder matrices. we also present the necessary and sufficient condition for the existonce of solution in the half meta posidve definite matrices for the inverse problem of matrix equation AX=B and obtain the general form of the solution.