微分在代数证明中的两个应用  

Two Applications of Differentiation in the Proof of Algebra

作　　者：申静 刘欢 SHEN Jing;LIU Huan(College of Science,Henan University of Technology,Zhengzhou 450001,China;School of Mathematics and Statistics,Zhengzhou University,Zhengzhou 450001,China)

机构地区：[1]河南工业大学理学院,郑州450001 [2]郑州大学数学与统计学院,郑州450001

出　　处：《大学数学》2022年第1期90-92,共3页College Mathematics

基　　金：河南工业大学博士基金(2020BS042);国家自然科学基金(11801525);郑州大学教研项目(2020zzuJXLX167)。

摘　　要：关于方阵特征值的代数重数大于等于几何重数这一结论,许多教材利用线性代数的知识已经给出证明,本文借助微分的观点证明了该结论.此外,利用微分证明了一个关于线性变换和向量积的恒等式,从而展示了微分在代数中应用的两个案例.In many textbooks,the conclusion that the algebraic multiplicity of the eigenvalues of square matrices is greater than or equal to the geometric multiplicity has been proved by using the knowledge of linear algebra,however,in this paper this conclusion is proved in the view of differentiation.In addition,an identity about linear transformation and vector cross product is proved by means of differentiation,thus showing two cases of the application of differentiation in algebra.

关 键 词：代数重数 几何重数 向量积 微分 

分 类 号：O151.2[理学—数学]