Let $m,n \in \mathbb{N}$. Let $T: \mathbb{R}^m \to \mathbb{R}^n$ be a [linear map](/page/Linear%20Map), and let $A=(A_{ij}) \in \mathbb{R}^{n \times m}$ be the standard matrix of $T$ with respect to the standard bases of $\mathbb{R}^m$ and $\mathbb{R}^n$. Then