A calculus of the absurd

18.1.4 Matrix multiplication

Multiplying two matrices is a strange and at first unfamiliar thing. The fundamental principle is that when we multiply two \(m \times n\) matrices \(A\) and \(B\), we obtain a new matrix, \(C\), whose \(j\)th entry in the \(i\)th row is defined as

\begin{equation} C_{ij} = \sum _{0 \leqq k \leqq j} A_{ik} B_{kj} \end{equation}