高等代数教学中关于“矩阵对角化”的一点注记

A Note on the Diagonalization of Matrix in Teaching of Advanced Algebra

矩阵对角化是高等代数中的基本内容,也是学习近世代数等后继课程所必须掌握的重要知识点之一。结合在高等代数教学过程中的体会,介绍了矩阵对角化的基本结论、矩阵对角化在矩阵计算等方面的应用和一类矩阵的对角化。对于不能对角化的矩阵,给出了化为"上三角矩阵"的条件。

Diagonalization of matrix is the basic comment in advanced algebra and is one of the necessary and important foundations in the studying of the subsequent courses such as numerical hnear algebra. Based on the personal experience in teaching advanced algebra, the basic results on diagonalization of matrix, its applications in the calculation of matrix and other aspects, and the diagonalization for a class of matrices are introduced. For the matrices that cannot be diagonalzed, we give the conditions for them to be upper triangular matrices.