Am×n矩阵的加边矩阵的奇异性问题

On Singularity of Bordered Matrix of any Matrix Am×n

中文摘要:

      给定m×n阶矩阵A,我们给出了它的加边矩阵M=[A B C O] (1)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M^-1=[A₁ B₂ C₃ O₄]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 。

英文摘要:

      In this paper the sufficient and necessary conditions of the nonsingularity of M are to be given.M=[A B C O] 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: M^-1=[A₁ B₂ C₃ O₄], 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 .