矩阵直积与拉直算子的有关性质及应用

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翻新时间：2023-06-03

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矩阵直积与拉直算子的有关性质及应用

摘要

本文介绍了矩阵直积的有关概念和性质,利用矩阵直积和拉直算子给出了线性矩阵方程有解的充分必要条件以及有惟1解的充分必要条件.然后将这些定理应用于解3种形式的线性矩阵方程.本文还讨论了矩阵直积和拉直算子在解矩阵微分方程中的1点应用,同时给出了矩阵微分方程解的形式.

关键词：矩阵直积；矩阵的拉直；线性矩阵方程；矩阵微分方程

The properties and applications of matrix direct product and straight operator

ABSTRACT

In this paper, some concepts and characters about matrix direct product have been introduced. With the matrix direct product and straightening operator, the necessary and sufficient conditions of the linear matrix equations have solutions and have unique one solution are given. Using these results, three types of Linear matrix equations are solved. In addition, in this paper, some applications of matrix direct product and straightening operator to solve matrix differential equations are discussed. And a matrix form solution of matrix differential equations is given.

Key words: matrix product; matrix realligned; Linear matrix equation; Matrix differential equation

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中文摘要、关键词……………………………………………………………………………1

英文标题………………………………………………………………………………………1

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正文

1 引言…………………………………………………………………………………2

2 矩阵直积有关概念及性质 …………………………………………………………3

2.1 矩阵直积的基本性质 …………………………………………………………………3

2.2 矩阵直积的特征值、特征向量及行列式 …………………………………5

2.2 矩阵拉直有关概念及性质 …………………………………………………8

3 矩阵直积的应用……………………………………………………………………………9