I think if in any context one uses the usual matrix algebra, it is the same linear map, just in a more abstract setting. If you tell me storing a lookup table

I think if in any context one uses the usual matrix algebra, it is the same linear map, just in a more abstract setting. If you tell me storing a lookup table is matrix, I think that is sort of out of context. But then again, I could be labelled a purist here, and I'm trying really hard to not fall into the trap.