A Riemannian geometry with complete geodesics for the set of positive semidefinite matrices of fixed rank | Zendy

Bart Vandereycken | Zendy; P.-A. Absil | Zendy; Stefan Vandewalle | Zendy

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A Riemannian geometry with complete geodesics for the set of positive semidefinite matrices of fixed rank

Author(s) -

Bart Vandereycken,

P.-A. Absil,

Stefan Vandewalle

Publication year - 2012

Publication title -

ima journal of numerical analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.672

H-Index - 66

eISSN - 1464-3642

pISSN - 0272-4979

DOI - 10.1093/imanum/drs006

Subject(s) - geodesic , rank (graph theory) , mathematics , euler's formula , combinatorics , set (abstract data type) , library science , geometry , computer science , mathematical analysis , programming language

We present a homogeneous space geometry for the manifold of symmetric positive semidefinite matrices of fixed rank. The total space is a connected part of the general linear group endowed with its natural right-invariant metric and the metric on the homogeneous space is chosen such that the quotient space is the image of a Riemannian submersion from the total space. As a result, we obtain complete...

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