矩阵秩分解定理的一个证明及其应用

矩阵的秩分解定理是矩阵论中的一个基础性定理.本文给出了秩分解定理的一个证明,描述了其中可逆矩阵P,Q的构造,讨论了秩分解定理及其P,Q的构造在解线性方程组中的应用,以及在判别Sylvester不等式等号成立中的应用.

A Proof of Rank Decomposition Theorem and its Applications

Rank decomposition theorem is a foundational theorem in matrics theory.In this paper,a brief proof of rank decomposition theorem is given,and the structures of two invertible matrics P and Q in this theorem are described.Then some applications of rank decomposition theorem and the structures of P,Q to solving system of linear equations and to discriminating equality in Sylvester's inequality are discussed.