不变性在线性代数中应用两例

Invariance and Its Application in Linear Algebra

本文介绍数学中“不变性”思想，讨论了线性代数中某种条件下秩数不变、特征多项式、特征值不变；对称性、半正定、正定性不变；以及度量性不变．以初等变换为首要方法，解决线性代数中一类重要问题．

In this paper, the thought of invariance in Mathematics has been introducted and the questions have been discussed which are about the invariance of Linear Algebra in certain condition, including matrix rank, eigenvalue polynomial, eigenvalue, symmetry, semipositive definite, positive definite and metric. The primary transform is used to solve a lot of important questions, such as finding matrix inversion and standard form. This makes us to catch easily the essence of transform about matrix and linear equation group.