I was taught to go element-by-element: element c_ij of the product = the linear combination a_ik*b_kj. What's presented here is the "same" but represents a high

I was taught to go element-by-element: element c_ij of the product = the linear combination a_ik*b_kj. What's presented here is the "same" but represents a higher level of abstraction, so that you think in terms of linear combinations of rows or columns, rather than linear combinations of scalars.