2-bit Walsh permutation

There are A002884(2) = 2 * 3 = 6 invertible binary 2×2 matrices.

They form the general linear group GL(3,2). It is isomorphic to the symmetric group S3 and the dihedral group D3 (see here).

overview transformation arrows transformed object
+ − + − + −


Cayley table

2×2 transformation matrices
2×2 transformation and 4×4 permutation matrices
all 3×3 permutation matrices
(same as 4×4 matrices without trivial fixed point)
one of the S3 subgroups of S4
This article is issued from Wikiversity. The text is available under Creative Commons Attribution-Share Alike 4.0 unless otherwise noted. Additional terms may apply for the media files.