This is easy to see in two dimensions, where a point on a circle
determines a compass direction, or equivalently, an angle <span class="math inline">\(\theta\)</span>).
Given an angle <span class="math inline">\(\theta\)</span>, a matrix can be defined, the
pre-multiplication by which rotates a point by an angle of <span class="math inline">\(\theta\)</span>.
For angle <span class="math inline">\(\theta\)</span> (in two dimensions), the <span class="math inline">\(2 \times 2\)</span> rotation
matrix is defi