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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"

$$A = \left(\begin{array}{cccc} a_{11} & a_{12} & \cdots & a_{1n}\\ a_{21} & a_{22} & \cdots & a_{2n}\\ \vdots & \vdots & \ddots & \vdots \\ a_{m1} & a_{m2} & \cdots & a_{mn}\\ \end{array}\right)$$

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

$$A=(a_{ij})_{ij}$$

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