Deterministic computation of the characteristic polynomial in the time of matrix multiplication


Séminaire AMAC: CASC

21/10/2021 - 15:00 Vincent Neiger (Sorbonne Université) IMAG 306

This talk describes joint work with Clément Pernet on an algorithm which computes the characteristic polynomial of a matrix over a field within the same asymptotic complexity, up to constant factors, as the multiplication of two square matrices. Previously, this was only achieved by resorting to genericity assumptions or randomization techniques, while the best known complexity bound with a general deterministic algorithm was obtained by Keller-Gehrig in 1985 and involves logarithmic factors. The new algorithm computes more generally the determinant of a univariate polynomial matrix in reduced form.