Uniform dilation ($D_s=sI$)

A uniform dilation about the origin multiplies every vector by one positive real scale $s$. The linear map $\mathbf{x}\mapsto s\mathbf{x}$ multiplies lengths by $s$ and $d$-dimensional volumes by $s^d$. This differs from stretching different axes by different factors. The case $s=1$ is the identity map.