On the angular metrics between linear subspaces

Yanxia Zhang; Li Qiu

doi:10.1016/j.laa.2006.08.015

On the angular metrics between linear subspaces

Yanxia Zhang, Li Qiu^*

^*Corresponding author for this work

School of Mathematics and Statistics

Hong Kong University of Science and Technology

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

Abstract

It has recently been shown that the symmetric gauge functions on the canonical (principal) angles give a family of unitarily invariant metrics between linear subspaces of the same dimension. In this short paper, we extend such metrics to subspaces of possibly different dimensions. This extension is necessary in addressing some perturbation analysis problems involving subspaces with different dimensions. Examples of such perturbation analysis problems are also studied in this paper using the extended metrics.

Original language	English
Pages (from-to)	163-170
Number of pages	8
Journal	Linear Algebra and Its Applications
Volume	421
Issue number	1
DOIs	https://doi.org/10.1016/j.laa.2006.08.015
Publication status	Published - 1 Feb 2007

Keywords

Canonical angles
Deficiency
Nullity
Perturbation
Subspaces
Unitarily invariant metric

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Zhang, Y., & Qiu, L. (2007). On the angular metrics between linear subspaces. Linear Algebra and Its Applications, 421(1), 163-170. https://doi.org/10.1016/j.laa.2006.08.015

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KW - Nullity

KW - Perturbation

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On the angular metrics between linear subspaces

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Keywords

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