FLINT3.7.0-dev
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fmpz_mat_hadamard

Synopsis#include <flint/fmpz_mat.h>
int fmpz_mat_hadamard(fmpz_mat_t A)source

Sets the square matrix AA of dimension nn to a Hadamard matrix and returns 1 if FLINT can construct one, and returns 0 otherwise. The constructions are Sylvester's for n=2vn = 2^v and Paley's for n=2v(q+1)n = 2^v(q + 1) and n=2v⋅2(q+1)n = 2^v \cdot 2(q + 1) with qq a prime power [Syl1867; Pal1933].

References#

  • [Syl1867] J. J. Sylvester, "Thoughts on inverse orthogonal matrices, simultaneous sign successions, and tessellated pavements in two or more colours, with applications to Newton's rule, ornamental tile-work, and the theory of numbers", Philosophical Magazine 34 (1867), 461–475.
  • [Pal1933] R. E. A. C. Paley, "On orthogonal matrices", Journal of Mathematics and Physics 12 (1933), 311–320. https://doi.org/10.1002/sapm1933121311
Cite this page

The FLINT team, “fmpz_mat_hadamard (fmpz_mat.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/fmpz_mat/fmpz_mat_hadamard.html (generated 2026-11-02).