The principal angles and the gap

Taslaman, Leo (2014) The principal angles and the gap. [MIMS Preprint]

[thumbnail of principalangle.pdf] PDF

Download (65kB)


In this note we provide proofs for some known results on the principal angles and the gap between two subspaces of $C^n$. Both the principal angles and the gap are introduced with respect to an arbitrary positive definite inner product. We show that the principal angles between two subspaces $U$ and $V$ are unique and prove that the largest one, $\theta_{\max}$, satisfies $\theta_{\max} = \max_{u\in U, \|u\|=1} \min_{v\in V, \|v\|=1} \angle(u,v)$ and $\sin\theta_{\max} =gap(U,V)$ when $\dim U=\dim V$.

Item Type: MIMS Preprint
Uncontrolled Keywords: principal angles, canonical angles, gap, canonical correlations
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 15 Linear and multilinear algebra; matrix theory
Depositing User: Leo Taslaman
Date Deposited: 03 Mar 2014
Last Modified: 20 Oct 2017 14:13

Actions (login required)

View Item View Item