“Mathematics is the art of reducing any problem to linear algebra.” This is a quote often attributed to William Stein, a former mathematics professor at the University of Washington, now the lead ...

Suppose we have a subspace \(\mathbb{S}\) of \(\mathbb{R}^n\) whose basis consists of \(k\) vectors \(\vec{v}_1,\vec{v}_2, \ldots , \vec{v}_k\). \[ \mathbb{S ...