矩阵秩的不等式及其在高等代数考研试题中的应用

Inequality of Matrix Rank and Its Application in Advanced Algebra Solving

矩阵的秩是反映矩阵固有特性的一个重要概念,矩阵秩的不等式应用则是求解试题中秩相关问题的关键,本文将利用分块矩阵、秩的理论、线性空间与线性变换以及方程组相关理论几个方面去求解高等代数考研试题中矩阵秩的不等式。

Rank of the matrix is an important concept to reflect the inherent properties of a matrix, and the inequality application of matrix rank is the key that solves the rank-related problems in the post-graduate exam. The paper makes use of the block matrix, the theory of rank, linear space and linear change and system of equations to solve the inequality of matrix rank in the exam of advanced algebra.