A lot of matrix concepts sound a lot more natural to me if I first think of what they mean in terms of vector spaces. For example, I think one can derive assoc

A lot of matrix concepts sound a lot more natural to me if I first think of what they mean in terms of vector spaces. For example, I think one can derive associativity of matrix multiplication less tediously from the observation that every matrix corresponds to a linear transform from a vector space to another, multiplication corresponds to function composition, and function composition is associative.