分块矩阵在《高等代数》考研试题中的应用

The Application of Block Matrix in the Examination Questions of Advanced Algebra

摘要: 分块矩阵是《高等代数》中的一个重要内容，也是《高等代数》考研试题中的题型之一。矩阵分块是处理阶数较高的矩阵时常采用的技巧，因此，探讨分块矩阵在《高等代数》考研试题中的应用有很好的现实意义。文章首先对分块矩阵的相关知识进行了简单阐述，然后重点对分块矩阵在考研试题中的应用从五个方面进行了探讨：从分块矩阵在行列式计算中的应用、在证明矩阵秩相关问题中的应用、在矩阵求逆问题中的应用、在特征值问题中的应用及在相似与合同中的应用五个方面进行分析，并用近年的考研真题进行了剖析，对数学与应用数学考研学生有一定的应用价值。

Abstract: Block matrix is an important content in Higher Algebra, and it is also one of the question types in Higher Algebra. Matrix partitioning is often used to deal with higher-order matrices, so it is of great practical significance to discuss the application of partitioning matrix in Advanced Algebra. Firstly, the article briefly expounds the related knowledge of block matrix, and then focuses on the application of block matrix in the examination questions from five aspects: this paper analyzes the application of block matrix in determinant calculation, in proof matrix rank correlation problem, in inverse matrix problem, in eigenvalue problem, and in similarity and contract, and uses the real questions in recent years to analyze, which has certain application value for mathematics and applied mathematics students.