可对角化矩阵的一个性质

A NATURE OF DIAGONALIZABLE MATRIX

方阵是否可以对角化,是矩阵的一条很重要的性质。对方阵可对角化的充要条件的理解,一直是线性代数学习中的一个困难问题。本文利用矩阵秩的相关结论,给出并证明了可对角化矩阵的一个性质。事实上,它也是可对角化矩阵的一个充分条件。

Whether square matrix can be digitalized is an important nature of matrix. The comprehension to the necessary and sufficient condition of square matrix has been a difficulty problem in linear algebra. In this paper, a nature of the diagonalizable matrix is given and proved by using relevant conclusions of the rank of matrix. In fact, it~ also a sufficient condition of diagonalizable matrix.