Eigenvalues and eigenvectors of matrix theory is an important component, the use of the knowledge of the matrix in the mathematical model can make the narrative more on simple white, clear, and eigenvalues and eigenvectors of the application, you can make mathematics calculation becomes more simple, clever. In writing this article, the first gives eigenvalues and eigenvectors of the concept, followed by a brief description of the method for finding it, and finally gives the eigenvalues and eigenvectors in the field of mathematics and other areas in some applications.