【摘要】 给定m×n阶矩阵A,我们给出了它的加边矩阵 为非奇的充分必要条件。其中O为r₁×r₂阶零矩阵。把M的逆矩阵记为分块形式 其中C₁为n×m、C₂为n×r₁、C₃为r₂×m、C₄为r₂×r₁阶矩阵。在一定条件下,我们证明了其中的C₁为A的广义逆矩阵A+。更多还原

【Abstract】 In this paper the sufficient and necessary conditions of the nonsingularity ofM are to be given. is the bordered matrix of any m x n order matrixA, where O is the zero matrix. The inverse matrix of M is experessed as theblocked fcrm: where C1 is n ×m order matrix, C2 is n×r1 ordermatrix, C3 is r2 × m order matrix, C4 is r2×r1 order matrix. Under certain conditions, we prove that C1 is the generalized inverse matrix of A, which defined as A+.更多还原