Base tensorielle des matrices de Hankel (ou de Toeplitz) Applications

Summary The set of all Hankel (or Toeplitz) matrices of dimensionn, is shown to possess tensorial bases: bases made ofn rank one matrices. Four families of such tensorial bases are possible. From this result, we deduce that the following computations can be performed with a number of multiplications of ordern instead of ordern ²: evaluation of the 2n+1 coefficients of the polynomial product of two polynomials of degreen, evaluation of the inverse of a lower triangular toeplitz matrix, evaluation of the quotient and of the remainder in the division of a polynomial of degree 2n by a polynomial of degreen.