The set homF2(F22,F22) can be identified with M2(F2) (matrices of size 2×2 with entries from F2). The association is not hard as every linear transformation corresponds to a matrix after you fix a basis. If you believe this, then it can be seen that |M2(F2)|=24=16.
How many elements in homF2(F22,F22)?
Course Queries Syllabus Queries 2 years ago
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2 years ago
My syllabus says that homF2(F22,F22)homF2(F22,F22) contains 16 elements. I’m guessing this is because F2×22F22×2 contains 16 elements, but I don’t see why this should be the reason.
It happens to be that we also have three bases for F22F22, so shouldn’t there be <16<16 linear maps? Some linear map could be represented by several matrix representations, i.e. some of the matrices in F2×22F22×2are similar.