A calculus of the absurd
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22.1.4 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
\(\seteqnumber{0}{22.}{9}\)\begin{equation} C_{ij} = \sum _{0 \leqq k \leqq j} A_{ik} B_{kj} \end{equation}