一类秩等方程的解

On the solutions of a class of equations of equirank

设K为一个体,K^(m×n)为K上m×n矩阵的集合.文中利用初等变换和广义逆刻画了体K上秩等方程rankA XY Z=rankA的几种情形解的存在性及其形式.

If K is supposed as any skew field and K^(m×n)denotes m×n matrices over K,the existence and expressions of solutions for a class of equations of equirank can be portrayed as rank〔A X Y Z〕=rank A in some cases.