Standard Matrix

The standard matrix $[T]$ of a Linear Transform $T:V\to W$ is the matrix formed by the Images of each Basis’ Column Vector. $[T]=[T(e_1),\dots ,T(e,n)]$

• Given $T:{\mathbb{R}}^n\to {\mathbb{R}}^m$, our standard matrix $[T]$ will have dimensions $m\times n$
• Element $[T_j]=T(e_j)$ where $e_j$ is the $j-th$ element of the Standard Basis

Example