2-bit Walsh permutation
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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 | |||
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+ | − | + | − | + | − |
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transformed objects in two directions | ||||
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vector | det. | arrows | as inverse | binary |
1 2 | + | ![]() |
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2 1 | − | ![]() |
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1 3 | + | ![]() |
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3 1 | − | ![]() |
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3 2 | + | ![]() |
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2 3 | − | ![]() |
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Cayley table
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![]() (same as 4×4 matrices without trivial fixed point) |
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