Jean-Christophe Bourin, Eun-Young Lee
We provide a complete structure theorem for involutory matrices. This yields a new approach to principal angles between subspaces and provide a series of nice formulae for these angles.
This paper contains 3 sections, 12 theorems, 72 equations.
Proposition 1.1
Let $P,Q\in\mathbb{M}_n$ be two nonzero orthoprojections, let $\mu_1\ge \cdots\ge \mu_n$ be the singular values of $PQ$, and let $r=\min\{\mathrm{rank\,} P,\mathrm{rank\,} Q\}$. Then there exists an orthonormal system $\{q_i\}_{i=1}^r$ in the range $\mathcal{Q}$ of $Q$, and an orthonormal system $\{ Furthermore we necessarily have: The principal angles $0\le \alpha_i^{\uparrow}\le \cdots\le \alph
