Does matrix rank makes sense modulo composite $n$?

Georgi Guninski on Sat, 18 Jul 2026 08:13:57 +0200

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Does matrix rank makes sense modulo composite $n$?

To: pari-dev@pari.math.u-bordeaux.fr
Subject: Does matrix rank makes sense modulo composite $n$?
From: Georgi Guninski <gguninski@gmail.com>
Date: Sat, 18 Jul 2026 09:13:40 +0300

Both pari and sage fail to compute the rank of matrix modulo composite $n$:
? M=Mod(1,4)*[2,2;2,2]
? matrank(M)
  ***   at top-level: matrank(M)
  ***                 ^----------
  *** matrank: impossible inverse in Fl_inv: Mod(2, 4).

Does matrix rank makes sense modulo composite $n$?

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