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矩阵的特征值与特征向量的应用摘要矩阵特征值与特征向量的讨论常被作为矩阵理论研究的主要对象和主要任务。具有重要意义，即研究如何求解矩阵对应的特征值与特征向量就具有很大的必要性也具有很强的实际意义。首先，本文简单介绍了矩阵特征值和特征向量的定义及性质，然后，在接下去的一章中介绍求解矩阵特征值与特征向量的五种求解方法，分别为定义法、列行互逆变换法、行初等变换法、列初等变换法及数学软件求解。并通过一些例题运用特征值与特征向量的性质和方法，使问题更简单，运算上更方便，是简化有关复杂问题的一种有效途径。最后，本文重点介绍了对特征值与特征向量的应用探究，阐述了特征值和特征向量在矩阵运算中的作用，在此我们着重以矩阵、特征值和特征向量为例来说明应用实例在高等代数教学中的作用。首先，介绍一些应用例子，如矩阵特征值在一阶常系数线性微分方程组中的应用及在马尔可夫链中的应用，尽量通过具体的应用实例来导出抽象的数学概念。其次，研究矩阵与特征值在人口模型中的应用和矩阵特征值与特征向量在建模中的一些应用。47197
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Matrix eigenvalue and eigenvector often used as the main object and the main task of matrix theory. Importance, namely how to solve the matrix corresponding to the eigenvalues and eigenvectors of great necessity also has a strong practical significance. Firstly, a brief definition of the characteristics and properties of the matrix and eigenvectors, and then, in the next chapter describes solving matrix eigenvalue and eigenvector five solving method were defined, Out line reciprocal transformation law, elementary row transformation, elementary column transformation and solving mathematical software. And through some examples using the properties and methods of the eigenvalues and eigenvectors of the problem easier and more convenient on operation, it is an effective way to simplify complex issues related. Finally, this article focuses on the eigenvalues and eigenvectors application inquiry to explain the role of the eigenvalues and eigenvectors of matrix operations, we focus on this matrix, the eigenvalues and eigenvectors an example to illustrate the application of higher instance Algebra teaching role. The first step, through a number of application examples, such as application eigenvalue and its application in a first-order linear differential equations with constant coefficients of the Markov chain, as far as possible through specific application examples to derive abstract mathematical concepts. The second step, and Matrix Eigenvalue and Eigenvalue and eigenvector some applications in population models in modeling, to form their own research.
毕业论文关键词： 矩阵；特征值；特征向量；人口模型；
Keywords: matrix; eigenvalue; eigenvector; population model;