一类矩阵方程的解及其应用  

Solutions to a Class of Matrix Equations and Their Applications

作　　者：方建卫 袁晖坪 FANG Jianwei;YUAN Huiping(School of Software,Chongqing Finance and Economics College,Chongqing 401320,China)

机构地区：[1]重庆财经学院软件学院,重庆401320

出　　处：《重庆工商大学学报（自然科学版）》2024年第6期121-125,共5页Journal of Chongqing Technology and Business University:Natural Science Edition

基　　金：国家自然科学基金(11271388);重庆市自然科学基金(CSTC2018JCYJAX0790)。

摘　　要：目前许多力学问题,如计算物理、地质学、结构设计、分子光谱学、电学、参数识别、自动控制、商务智能、线性系统理论、大数据分析与动态分析等领域,都要依赖于矩阵方程。研究了矩阵方程AX=B的求解问题,给出了矩阵方程AX=B有解的新判别条件及其通解表达式,推广了矩阵方程AX=B的判解条件和通解形式;例题表明简化了矩阵方程AX=B的求解过程,同时也简化了向量组的线性表示式和基到基的过渡矩阵计算,这对于充实矩阵方程的求解理论和简化计算均是有益的。Matrix equations are crucial in solving many problems in various fields such as mechanics,computational physics,geology,structural design,molecular spectroscopy,electrical engineering,parameter identification,automatic control,business intelligence,linear system theory,big data analysis,and dynamic analysis.This study investigates the solution of the matrix equation AX=B,providing new criteria for the existence of solutions and their general expressions.It extends the conditions for solvability and the general forms of the solutions of the matrix equation AX=B.Examples demonstrate that this approach simplifies the solution process of the matrix equation AX=B,as well as the calculation of linear representations of vector sets and the transition matrix between bases.This contributes to enriching the solution theory of matrix equations and simplifying computations.

关 键 词：初等变换 矩阵方程 通解 线性表示 过渡矩阵 

分 类 号：O151.21[理学—数学]