矩阵的左,右逆及其表达式

本文讨论左、右逆阵及其存在的充要条件，借助于Ｍｏｏｒｅ－Ｐｅｎｒｏｓｅ广义逆，给出矩阵左、右逆的简洁表达式，从而为矩阵分析与应用提供便利。

关于矩阵特征多项式的几个性质

设P为秩为r的矩阵,而A,B皆为方阵,它们的特征多项式分别为fA(λ)和fB(λ),若满足AP=PB,则有fB(λ)满足fA(λ)。本文进一步就P的不同情况进行讨论,得到矩阵特征多项式对应的其他性质。

On a Matrix Equation AX+XB=C over a Skew Field

In this paper we study a matrix equation AX+BX=C(I)over an arbitrary skew field,and give a consistency criterion of(I)and an explicit expression of general solutions of(I).A convenient,simple and practical method of solving(I)is also given.As a particular case,we also give a simple method of finding a system of fundamental solutions of a homogeneous system of right linear equations over a skew field.