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

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## Abstract

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 |
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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 |

URI: | https://eprints.maths.manchester.ac.uk/id/eprint/2105 |

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