从两道习题看矩阵可对角化的判定

Criteria for Diagonalizable Matrices via Two Examples

分别利用特征向量、特征子空间、特征值重数、极小多项式和Jordan标准形的基本概念,得出判定矩阵可否对角化的五种准则,并将其用于两道习题的多种证明.

Using basic concepts , such as eigenvectors , eigenspaces , multiplicities of eigenvalues ,minimal polynomials , and Jordan canonical forms , one can get five criteria for diagonalizable matrices .In this paper ,we apply these criteria to two examples ,and explore intrinsic relationships between these criteria .