The online calculator calculates the eigenvalues of the matrix with the Denton, Parke, Tao, Zhang approach. The algorithm from Denton, Parke, Zhang uses the eigenvector-eigenvalue identity. The eigenvector-eigenvalue identity dosn't need the solution of a equation system. The algorithm uses the sub-matrices to calculate the magnitude of the eigenvectors.
Enter the matrix elements for matrix A: a1,1, a1,2, ...
Step-by-step calculation of the eingenvectors with the Denton, Parke, Tao, Zhang approach.
If A is an n×n Hermitian matrix with eigenvalues λ1(A),…,λn(A) and i,j=1,…,n, then the j-th component vi,j of a unit eigenvector vi associated to the eigenvalue λi(A) is related to the eigenvalues λ1(aj),…,λn−1(aj) of the minor aj of A formed by removing the j-th row and column by the formula