On the Geometry and Quantization of Manifolds of Positive Semi-Definite Matrices Journal Article uri icon

Overview

abstract

  • The geometry of different spaces of positive semi-definite matrices buffeted by rank and trace constraints is studied. In addition to revealing their Riemannian structure, we derive the normalized volume of a ball over these spaces. Further, we use the leading coefficient from the ball volume expansion to bound the quantization error incurred with finite-sized sphere-packing codebooks as well as random codebooks to represent sources distributed over general Riemannian manifolds.

publication date

  • January 1, 2013

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Additional Document Info

start page

  • 1

end page

  • 1

volume

  • PP

issue

  • 99