fmpz_mat_is_spd
Synopsis
#include <flint/fmpz_mat.h>int fmpz_mat_is_spd(const fmpz_mat_t A)sourceReturns 1 if A is symmetric positive definite and 0 otherwise. The answer is proven.
After checking symmetry, the function tries an LDL^T decomposition in ball arithmetic (arb_mat_ldl) at precisions doubling from 32 bits up to four times the size of the entries; if that does not certify positive definiteness, it decides exactly from the signs of the coefficients of the characteristic polynomial (Descartes' rule of signs).
Cite this page
The FLINT team, “fmpz_mat_is_spd (fmpz_mat.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/fmpz_mat/fmpz_mat_is_spd.html (generated 2026-10-20).
@misc{flint-doc-fmpz-mat-fmpz-mat-is-spd,
author = {{The FLINT team}},
title = {{fmpz\_mat\_is\_spd (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_is_spd.html},
note = {Generated 2026-10-20}
}