【摘要】 利用两个矩阵的奇异值分解(P-SVD)以及广义逆矩阵的性质,研究了两个矩阵乘积的{1,2,3}逆-和{1,2,4}逆-的反序律,得到了(AB){1,2,3}■ B{1,2,3}A{1,2,3}以及(AB){1,2,4}■ B{1,2,4}A{1,2,4}成立的充要条件,并获得了(AB){1,2,3}=B{1,2,3}A{1,2,3}以及(AB){1,2,4}=B{1,2,4}A{1,2,4}的等价条件。更多还原

【Abstract】 The reverse order laws for {1,2,3}-inverse and {1,2,4}-inverse of product of two matrices are studied by applying the product singular value decomposition P-SVD and the characters of generalized inverse.The necessary and sufficient conditions of(AB){1,2,3}■ B{1,2,3}A{1,2,3} and(AB){1,2,4}■ B{1,2,4}A{1,2,4}are obtained.Then equivalent conditions of(AB){1,2,3}=B{1,2,3}A{1,2,3} and(AB){1,2,4}=B{1,2,4}A{1,2,4} are obtained.更多还原