The properties of eigenvalue and its application in postgraduate entrance examination mathematics

The eigenvalue and eigenvector of matrix is one of the key contents of linear algebra,and it is also the hot spot of postgraduate entrance examination. Candidates should be careful and careful when reviewing this content. The first step is to understand the concept of eigenvalues and eigenvectors, and master the method of solving eigenvalue and eigenvector of matrix.Secondly, we should understand the concept of matrix similarity, master the related properties, understand the conditions of matrix similarity diagonalization, and master the method of matrix similarity diagonalization.Finally, we must be familiar with the special properties of eigenvalues and eigenvectors of real symmetric matrices, and master the method of transforming real symmetric matrices into diagonal matrices by using orthogonal matrices. (Abstract)