Faddeev-LeVerrier algorithm

The Faddeev-LeVerrier algorithm is a recursive method in linear algebra for computing the coefficients of the characteristic polynomial of a square matrix. Once the polynomial is known, its roots give the eigenvalues of the matrix, and by the Cayley-Hamilton theorem the matrix itself satisfies the polynomial. Unlike working directly from the definition of the determinant, which brings in a symbolic quantity, the method operates on the entries of the matrix and builds the coefficients one after another from an auxiliary sequence of matrices and traces of matrix powers. The same recursion also yields the determinant and, when the matrix is invertible, its inverse. The method carries two names because it was rediscovered several times: Urbain Le Verrier published it first in 1840, and it was later redeveloped by P. Horst, Jean-Marie Souriau, Faddeev and Sominsky, and J. S. Frame, among others.