Three interpretations of matrix products
0. Prerequisites and notations
1. Interpretation #1: Weighted sum of columns or rows
1.1 Matrix vector product as a weighted sum of columns
1.2 Vector matrix product as a weighted sum of rows
2. Interpretation #2: Dot products of columns or rows with input vector
2.1 Matrix vector product as a dot product of rows with input vector
2.2 Vector matrix product as a dot product of columns with input vector
3. Interpretation #3: Matrix-matrix product as the sum of outer products