两个矩阵和的{1,3}-逆与{1,4}-逆

On {1,3}-inverse and {1,4}-inverse matrix of sum of two matrices

利用矩阵的秩方法与广义Schur补的最大秩与最小秩,研究两个矩阵和的{1,3}-逆与{1,4}-逆分别与各个矩阵的{1,3}-逆与{1,4}-逆的和之间的关系.得到{A^((1,3))+B^((1,3))}={(A+B)^((1,3))}以及{A^((1,4))+B^((1,4))}={(A+B)^((1,4))}成立的充要条件.

The relation between{1,3}-inverse and{1,4}-inverse of sum of two matrices and the sum of{1,3}-inverse and{1,4}-inverse of every matrix was studied by using matrix rank method and maximal ranks and minimal ranks of generalized Schur complement.The necessary and sufficient conditions of{A^((1,3))+B^((1,3))}={(A+B)^((1,3))}and{A^((1,4))+B^((1,4))}={(A+B)^((1,4))}were obtained.