matrix decomposition theorem

Let P be a matrix of eigenvectors of a given square matrix A and D be a diagonal matrix with the corresponding eigenvalues on the diagonal. Then, as long as P is a square matrix, A can be written as an eigen decomposition A = P D P^(-1), where D is a diagonal matrix. Furthermore, if A is symmetric, then the columns of P are orthogonal vectors.

eigen decomposition | eigenvalue | eigenvector | singular value decomposition