Subspace Principal Angle Preserving Property of Gaussian Random Projection

Jiao, Yuchen; Shen, Xinyue; Li, Gen; Gu, Yuantao

doi:10.1109/dsw.2018.8439111

Cited by 4 publications

(1 citation statement)

References 27 publications

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“…Many distinct concepts of angle between subspaces can be found in the literature [Dix49,Fri37,Glu67,Jor75,Wed83], having applications in geometry, linear algebra, and other areas as diverse as functional analysis [KJA10], statistics [Hot36] and data mining [JSLG18]. Some recent works on the subject can be found in [BT09,GH06,GNSB05,Hit10].…”

Section: Introductionmentioning

confidence: 99%

Grassmann angles between real or complex subspaces

Mandolesi

2019

Preprint

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The Grassmann angle unifies and extends several concepts of angle between subspaces found in the literature, being defined for subspaces of equal or different dimensions, in a real or complex inner product space. It is related to Grassmann's exterior algebra and to the Fubini-Study and Hausdorff distances, and describes how Lebesgue measures contract under orthogonal projections. This angle is asymmetric for subspaces of different dimensions, turning the total Grassmannian of all subspaces into a quasipseudometric space. Other odd characteristics, already present in former angle concepts but usually overlooked, are explained, like its behavior with respect to orthogonal complements and realifications. We use it to study the Plücker embedding of Grassmannians, and to get an obstruction on complex structures for pairs of subspaces.

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