Matrix Multiplication

In this section, I will cover matrix multiplication. My objective is to explain why the matrix multiplication \(C = A \cdot B\) uses this expression to calculate the \(c_{ij}\) entry:

\[ c_{ij} = a_{i1} \cdot b_{1j} + a_{i2} \cdot b_{2j} + \ldots + a_{in} \cdot b_{nj} = \sum\limits_{k = 1}^{n} a_{ik} \cdot b_{kj}, \]

where \(A\) is an \((m \times n)\) matrix and \(B\) is an \((n \times p)\) matrix.