Matrix Diagonalization

 A vectorv is called an eigenvector of a matrix A with an eigenvalue λ, if Av=λv. Matrix diago-nalization means finding all eigenvalues λ iand (op-tionally) eigenvectors vi of the matrix A. If A is hermitian,A†=A, then its eigenvalues are real and its eigenvectors V={v1, . . . ,vn} form a full basis where the matrix A is diagonal,V TAV= Λ, where Λ is a diagonal matrix with eigenvalues λi along the diagonal. In the following we shall only consider real symmetric matrices.

 https://phys.au.dk/~fedorov/Numeric/08/eigen.pdf