特殊矩阵的特征值性质

The Eigenvalue of Special Matrix

在高等代数中矩阵是研究问题很重要的工具,在讨论矩阵的性质时给出了矩阵特征值的定义,但对矩阵特征值的性质研究很少,对特殊矩阵的特征值性质的研究更少,而特殊矩阵的特征值对研究特殊矩阵有很重要的意义。我们在研究矩阵及学习有关数学知识时,经常要讨论一些特殊矩阵的性质。为此,本文围绕幂等矩阵、反幂等矩阵、对合矩阵、反对合矩阵、幂零矩阵、正交矩阵、对角矩阵、可逆矩阵等特殊矩阵给出了其主要性质并加以证明,为广大读者学习矩阵时提供参考。

Matrix is an important tool for studying problems in Advanced Algebra. The eigenvalue is defined when discussing the character of matrix, but the eigenvalue of matrix is little studied, and the eigenvalue of especial matrix much less studied, however, the eigenvalue of special matrix has important meaning during studying it. We often need to discuss special matrix when studying matrix and other math knowledge related to matrix. Therefore, in order to offer reference to readers, based on idempotent matrix, antiidempotent matrix, involutory matrix, antiinvolutory matrix, nilpotent matrix, orthogonal matrix, diagonal matrix, invertidle matrix, the main character of special matrix are proved in this paper.