# A calculus of the absurd

### Chapter 22 Linear algebra

#### 22.1 Properties of matrices

On the off-chance that someone other than me reads these, please don’t read this section in one go; it’s here for reference.

##### 22.1.1 Introduction

A matrix has $$m$$ rows and $$n$$ columns. For example, a $$2 \times 3$$ matrix would look something like this

$$\begin{pmatrix} 0 & 1 & 2 \\ 3 & 5 & 8 \end {pmatrix}$$

Of course, the values in a matrix can be anything. If we want to denote a matrix having only real numbered elements, we can write this as $$\mathbb {R}^{m \times n}$$ (we can also do the same for other sets, for example $$\mathbb {N}^{m \times n}$$ for an $$m$$ by $$n$$ matrix whose elements are all natural numbers).

We can also define a matrix using the notation

$$(f(i, j))_{ij}$$

This means that the $$j$$th column of the $$i$$th row is equal to $$f(i, j)$$.