有理矩阵有理对角化问题的算法及程序设计研究报告

摘要

Matrix is an important mathematical method of diagonalization, but because of its computational complexity, it has caused great difficulties on the application, The mathematical software has the function of processing of diagonalization, but for rational matrix diagonalization problem in the field of rational number the result is not satisfactory. So the study of rational matrix over the rational number field similarity diagonalization diagonalization, contract and orthogonal diagonalization algorithm and program project, design to realize rational matrices over the field of rational numbers on the diagonalization of utility software, solves the rational matrices over the field of rational numbers on the diagonalization of the accurate determination and computation problem.%　　矩阵对角化是重要的数学方法，但因其计算复杂却造成了应用上的极大困难，虽然已有的数学软件具有处理对角化功能，但对有理矩阵在有理数域上的对角化问题的计算结果却不尽人意。所以提出了研究有理矩阵在有理数域上相似对角化、合同对角化以及正交对角化的算法与程序课题，设计出能够实现有理矩阵在有理数域上对角化的实用软件，解决了有理矩阵在有理数域上对角化的精确判定与计算问题。