# A calculus of the absurd

##### 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

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