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Course Queries Syllabus Queries 2 years ago
Posted on 16 Aug 2022, this text provides information on Syllabus Queries related to Course Queries. Please note that while accuracy is prioritized, the data presented might not be entirely correct or up-to-date. This information is offered for general knowledge and informational purposes only, and should not be considered as a substitute for professional advice.
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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.
The set homF2(F22,F22)homF2(F22,F22) can be identified with M2(F2)M2(F2) (matrices of size 2×22×2 with entries from F2F2). 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|M2(F2)|=24=16.
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