可交换矩阵成立的条件与性质

可交换矩阵成立的条件与性质

摘要：矩阵是高等数学中1个重要内容，在数学领域以及其他科学领域有着重大的理论意义。众所周知，矩阵的乘法在1般情况下是不满足交换律的，即在通常情况下，AB≠BA。但是，在某些特殊情况下，矩阵的乘法也能满足交换律。可交换矩阵有着很多特殊的性质和重要的作用。本文从可交换矩阵和相关知识的定义出发，探讨了矩阵可交换的1些条件和可交换矩阵的部分性质，并且介绍了几类特殊的可交换矩阵。

关键词：矩阵；可交换；条件；性质；上3角矩阵

The Conditions For The Commutation of Matrix and some properties of The Commutative Matrix

Abstract：Matrix, a important content in altitude-mathematics, has a great theoretic significance in the aspect of both mathematics and other science field. As far as we have concerned, the multiplication of matrix could not satisfy the exchange rule under the normal condition, that is to say, normally, AB≠BA . Whereas, in some certain conditions, the multiplication of matrix could satisfy the exchange rule. The exchangeable matrix has many special properties and important effection. This paper discusses some conditions of the matrix exchange and part of the property of the exchangeable matrix , and also introduces several kinds of specific exchangeable matrix. All of these are discussed from the concept of exchangeable matrix and relative information.

Key Words：Matrix;interchangeable;conditions;property;upper triangular matrix

目 录

前 言…………………………………………………………… 1

1. 矩阵可交换的条件…………………………………………… 2

2. 可交换矩阵的性质…………………………………………… 6

3. 几类常用的可交换矩阵……………………………………… 8

总 结…………………………………………………………… 14

参 考 文 献……………………………………………………… 15

致 谢…………………………………………………………… 16

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