fmpz_mat_similarity
Synopsis
#include <flint/fmpz_mat.h>void fmpz_mat_similarity(fmpz_mat_t A, slong r, fmpz_t d)sourceReplaces the square matrix A by P^{-1} A P, where P is the identity matrix with the entries in row r and every column j \notin \{r - 1, r\} replaced by d. Requires 0 \le r < n.
Equivalently, d times column r is added to every column j \notin \{r - 1, r\}, and then d times the sum of the rows j \notin \{r - 1, r\} is subtracted from row r. Such transforms preserve the determinant and the characteristic and minimal polynomials.
Cite this page
The FLINT team, “fmpz_mat_similarity (fmpz_mat.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/fmpz_mat/fmpz_mat_similarity.html (generated 2026-10-20).
@misc{flint-doc-fmpz-mat-fmpz-mat-similarity,
author = {{The FLINT team}},
title = {{fmpz\_mat\_similarity (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_similarity.html},
note = {Generated 2026-10-20}
}