In mathematics (linear algebra), the Faddeev–LeVerrier algorithm is a recursive method to calculate the coefficients of the characteristic polynomial of a square matrix, A, named after Dmitry Konstantinovich Faddeev and Urbain Le Verrier. Calculation of this polynomial yields the eigenvalues of A as its roots; as a matrix polynomial in the matrix A itself, it vanishes by the fundamental Cayley–Hamilton theorem. Computing determinant from the definition of characteristic polynomial, however, is computationally cumbersome,because is new symbolic quantity, whereas this algorithm works directly with coefficients of matrix .