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 | |||
---|---|---|---|---|---|
+ | − | + | − | + | − |
transformed objects in two directions | ||||
---|---|---|---|---|
vector | det. | arrows | as inverse | binary |
1 2 | + | |||
2 1 | − | |||
1 3 | + | |||
3 1 | − | |||
3 2 | + | |||
2 3 | − |