Epsilons, no. 2: Understanding matrix multiplication

The geometric and algebraic interpretation of matrix products

Matrix multiplication is not easy to understand.

Even looking at the definition used to make me sweat, let alone trying to comprehend the pattern. Yet, there is a stunningly simple explanation behind it.

Let's pull back the curtain!

First, some notations.

The product of A and B is given by the following formula. Not the easiest (or most pleasant) to look at.