fmpz_mat_charpoly_bound
Synopsis
#include <flint/fmpz_mat.h>void fmpz_mat_charpoly_bound(fmpz_t bound, const fmpz_mat_t A)sourceSets bound to an upper bound for the absolute values of the coefficients of the characteristic polynomial of the square matrix A.
The coefficient of x^{n-k} is \pm the sum of the \binom{n}{k} principal k \times k minors. By Hadamard's inequality each minor is at most the product of the k largest row norms of A, and also of the k largest column norms. The function returns the smaller of the maxima over k of \binom{n}{k} times these products.
Guides#
Cite this page
The FLINT team, “fmpz_mat_charpoly_bound (fmpz_mat.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/fmpz_mat/fmpz_mat_charpoly_bound.html (generated 2026-10-20).
@misc{flint-doc-fmpz-mat-fmpz-mat-charpoly-bound,
author = {{The FLINT team}},
title = {{fmpz\_mat\_charpoly\_bound (fmpz\_mat.h)}},
howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
year = {2026},
url = {https://flintlib.org/doc/fmpz_mat/fmpz_mat_charpoly_bound.html},
note = {Generated 2026-10-20}
}