Block Diagonalization and a Numerical Method of the Eigenproblem for an n×n Normal Matrix

It is important that the eigenproblem of a matrix is solved in the matrix analysis and its engineering application. For a normal matrix with multiplex eigenvalues, a method of block diagonalization is given by using Householder transformation and finding eigenvectors of the tridiagonal Hermitian matrix. On the basis of this, a numerical method of finding its eigenvalues and eigenvectors is obtained.