Matrix

Definition: Matrix

An $m\times n$-matrix $A\in F^{m\times n}$ over a field $F$ is a rectangular array of elements $a_{ij}$ from $F$, where $m$ is the number of rows, $n$ is the number of columns and $a_{ij}\in F,1\le i\le m,1\le j\le n$.

$$\left[\begin{array}{cccc}{a}_{11}& a_{12}& \cdots & a_{1n}\\ a_{21}& a_{22}& \cdots & a_{2n}\\ ⋮& ⋮& \ddots & ⋮\\ a_{m1}& a_{m2}& \cdots & a_{mn}\end{array}\right]$$

NOTATION

Matrix names are usually capital letters from the Latin alphabet: $A,B,C,$ etc.

The actual matrix can be denoted either by square $[]$ brackets or parentheses $()$.