[algernonramone]

I am willing to admit that I find matrix multiplication ugly, as well as non-intuitive. But, I am also willing to admit that my finding it ugly is likely a result of my relative mathematical immaturity (despite my BS in math).

[znkr]

Maybe it helps to think of matrix multiplication as a special case of the composition of linear transformation. In the finite dimensional case they can be expressed as matrix multiplications.