m矩阵的判定及其应用.doc

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本科生毕业论文
M矩阵的判定及其应用
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数学与应用数学
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2012 年 4 月
长沙学院本科生毕业论文
M矩阵的判定及其应用
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指导教师: 讲师


2012 年 4 月
摘要
M矩阵是重要的特殊矩阵之一,并且M矩阵在计算数学,生物学,物理学,、性质等基本知识,系统地归纳总结了M矩阵的三种判定方法:用M矩阵的定义判定,,通过分析比较得到:低阶矩阵用M矩阵的定义判定比较简单,,,,本文还介绍了M矩阵在实际问题中的一些应用,主要讨论了M矩阵在经济学“投入—产出模型”中的Leontief开模型和Leontief闭模型的应用.
关键词:M矩阵,Z矩阵,三角分解,Leontief模型
ABSTRACT
M matrix is one of the important special matrixes, and it is widely used putational mathematics, biology, physics, intelligent science, economics and others fields. This paper introduces some basic knowledge such as the definition and characters of M matrix and systematically summarizes three kinds of methods to judge M matrix: through the definition of M matrix to judge, applying triangle position method to judge, and using generalized positive definite matrix method to judge. As for M matrix with different orders, we can select a simple corresponding method to judge, through the analysis parison, we can summarize that: the low order matrix judged by the definition of M matrix is simpler, the high order matrix using triangle position method and generalized positive definite matrix method is simpler. Triangular Factorization can be posed into an upper triangular matrix and a lower triangular matrix, reduce the form of matrix. The generalized positive definite matrix deompstion method will divide the high order matrix into several pieces; make the order of matrix lower. In addition, this paper also introduces some applications of M matrix in practical problems, it mainly discusses the application of M matrix in the Leontief open model and the Leontief closed model of "investment-output model" in economics.
Keywords: M matrix, Z matrix, Triangular position, The Leontief model
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