The Study of Root Subspace Decomposition between Characteristic Polynomials and Minimum Polynomial  

作　　者：Lilong Kang Yu Wang Yingling Liu Lilong Kang;Yu Wang;Yingling Liu(College of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong, China)

机构地区：[1]College of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong, China

出　　处：《Open Journal of Applied Sciences》2024年第7期1637-1647,共11页应用科学（英文）

摘　　要：Let Abe the linear transformation on the linear space V in the field P, Vλibe the root subspace corresponding to the characteristic polynomial of the eigenvalue λi, and Wλibe the root subspace corresponding to the minimum polynomial of λi. Consider the problem of whether Vλiand Wλiare equal under the condition that the characteristic polynomial of Ahas the same eigenvalue as the minimum polynomial (see Theorem 1, 2). This article uses the method of mutual inclusion to prove that Vλi=Wλi. Compared to previous studies and proofs, the results of this research can be directly cited in related works. For instance, they can be directly cited in Daoji Meng’s book “Introduction to Differential Geometry.”Let Abe the linear transformation on the linear space V in the field P, Vλibe the root subspace corresponding to the characteristic polynomial of the eigenvalue λi, and Wλibe the root subspace corresponding to the minimum polynomial of λi. Consider the problem of whether Vλiand Wλiare equal under the condition that the characteristic polynomial of Ahas the same eigenvalue as the minimum polynomial (see Theorem 1, 2). This article uses the method of mutual inclusion to prove that Vλi=Wλi. Compared to previous studies and proofs, the results of this research can be directly cited in related works. For instance, they can be directly cited in Daoji Meng’s book “Introduction to Differential Geometry.”

关 键 词：Characteristic Polynomial Minimum Polynomial Root Subspace 

分 类 号：O17[理学—数学]