Title :
Embedded geometry of the set of symmetric positive semidefinite matrices of fixed rank
Author :
Vandereycken, Bart ; Absil, P.-A. ; Vandewalle, Stefan
Author_Institution :
Dept. of Comput. Sci., Katholieke Univ. Leuven, Leuven, Belgium
Abstract :
This paper deals with the Riemannian geometry of the set of symmetric positive semidefinite matrices of fixed rank. This set is studied as an embedded submanifold of the real matrices equipped with the usual Euclidean metric. With this structure, we derive expressions of the tangent space and geodesics of the manifold, suitable for efficient numerical computations.
Keywords :
geometry; matrix algebra; set theory; Euclidean metric; Riemannian geometry; embedded geometry; embedded submanifold; fixed rank; numerical computation; symmetric positive semidefinite matrix; Computer science; Control systems; Eigenvalues and eigenfunctions; Euclidean distance; Focusing; Geometry; Geophysics computing; Interpolation; Symmetric matrices; Riemannian geometry; Symmetric positive semidefinite matrices; geodesics; low rank;
Conference_Titel :
Statistical Signal Processing, 2009. SSP '09. IEEE/SP 15th Workshop on
Conference_Location :
Cardiff
Print_ISBN :
978-1-4244-2709-3
Electronic_ISBN :
978-1-4244-2711-6
DOI :
10.1109/SSP.2009.5278558
