`fmpz_mat_similarity`

Synopsis#include <flint/fmpz_mat.h>

void fmpz_mat_similarity(fmpz_mat_t A, slong r, fmpz_t d)source

Replaces 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 2026-11-02).

@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 2026-11-02}
}

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