Uniform dilation
= Uniform dilation
{title2=$D_s=sI$}
= Dilation
{synonym}
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>.