判定线性代数中矩阵相似关系的原理和方法

The Principle and Method with Identification Similar Relationships of Matrices in Linear Algebra

指出教育部考试中心2019版考研数学考试分析中关于矩阵相似试题解答中的一个错误.系统梳理了高等代数和线性代数课程中关于相似矩阵刻画的角度和方法,明确了在线性代数课程体系中3类可以作出相似判定的矩阵类别及其对应的判别方法,给出不能一般判定相似关系的第4类矩阵的基本特征,并结合实例给出在特殊情形下解决第4类矩阵相似关系判定的方法.

This paper points out a mistake in the analysis of similar matrix test questions in the examination of Mathematics for postgraduate entrance examination of the examination center of the Ministry of Education in 2019 edition.It systematically combs the angles and methods of describing similar matrices in the courses of advanced algebra and linear algebra and defines three kinds of matrices which can make similar judgments in the course system of linear algebra.The basic characteristics of class 4 matrices which can′t judge the similarity relation in general are given by the corresponding discriminant method,and the methods to determine the similarity relation of class 4 matrices in special cases is given by an example.