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A Riemannian geometry with complete geodesics for the set of positive semidefinite matrices of fixed rank
2012
IMA Journal of Numerical Analysis
We present a homogeneous space geometry for the manifold of symmetric positive semidefinite matrices of fixed rank. The total space is the general linear group endowed with its natural rightinvariant 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 geodesics that are the image of certain geodesics on the general linear group. We derive in addition an efficient
doi:10.1093/imanum/drs006
fatcat:jeu2kstwcfcivl4u27twivg3ky