On the Eigenvalues and Eigenvectors
Abstract
Matrix is the main research tools of linear algebra and advanced algebra and universities play a vital role in mathematics.Eigenvalues and Eigenvectors of "advanced algebra" and "Linear Algebra" course an important basic elements,it In many areas has been widely used.
This thesis focuses on the matrix eigenvalue and eigenvector of the concept,nature,method and system application issues related to induction,so we Eigenvalues and eigenvectors have further understanding.First of all,discusses the matrix eigenvalue and eigenvector of the concepts and some properties.Secondly,the matrix eigenvalue and eigenvector method to examine the main conclusion of the three solutions,the first is the most basic method,but the process is relatively complex; the second is a more simple solution,the method allows us to solve problems more quickly,saving time; third as a special solution,the special method used when appropriate,can become easy to solve.The latter two are elementary transformation of matrix theory to the eigenvalues of a matrix,and then observed directly derived feature vector,feature vector can be said with Eigenvalues method is synchronized to calculate a lot less.Finally,the elaborated matrix eigenvalue and eigenvectors.not only can use Eigenvalues and eigenvectors of nature to solve the problem,and use of matrix eigenvalues and eigenvectors can be translated into standard quadratic form,such as the matrix diagonalization,the paper will use advanced algebra,linear algebra specific examples of knowledge combined with a detailed discussion.on the matrix eigenvalue and eigenvector applications in other areas,we also need to be explored in depth study.