Given a field $\mathbb{K}$ (generally $\mathbb{R}$ or $\mathbb{C}$), a matrix of order $m\times n$ with coefficients in $\mathbb{K}$ is a "box"

made up by $mn$ elements of $\mathbb{K}$ arranged in $m$ rows and $n$ columns. We denote by $a_{ij}$ the element positioned in the row $i$ and column $j$. It is also used the notation

which means in the row $i$ and column $j$ one finds the number $a_{ij}$