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So based on the last bullet the idea that affine exists more in the real world, and linear is what we need to program with, so we perform magic to translate? I guess why do we prefer one over the other?


I'm getting a little confused between functions, vectors and maps. Earlier, we said that we can think of functions as vectors because they follow the "rules" of a vector subspace (we just have to tweak our definitions). Here, are we describing functions as maps? And if so, is it possible to describe vectors as maps (through functions)?


According to the second bullet point, in other words, all linear maps must be that f(0) = 0?


What is the use of affine functions? Is there anything helpful or interesting about them? Also, is there any interesting use for them in graphics?


Does this mean that linear map and linear function are interchangeable terms?