矩阵对角化及其应用

矩阵对角化及其应用

摘 要：本文综述了矩阵可对角化和可同时对角化的条件,讨论了可对角化矩阵的基本性质和结论,给出了矩阵对角化在矩阵计算,行列式计算,常微分方程问题等方面的应用.

关键词：矩阵;对角化;对称矩阵;循环矩阵;反循环矩阵;矩阵同时对角化.

Matrix Diagonolization and Application

Abstract: In this paper, the conditions of matrix diaholizable and simultaneous diagonolizable have been summarized.The properties and results of diagonal matrices have been discussed .The applications of matrix diagonolization in matrix computation,determinant computation and solving ordinary differential equation have been given.

Keywords:Matrix;Diagonolization;Symmetric matrix;Circular matrix;contra-circular matrix;Simutaneous diagonolization.