Intrinsic volumes of symmetric cones

Abstract

We compute the intrinsic volumes of the cone of positive semidefinite matrices over the real numbers, over the complex numbers, and over the quaternions, in terms of integrals related to Mehta's integral. Several applications for the probabilistic analysis of semidefinite programming are given.

42 pages

References in corpus (1)

• Large Deviations of Extreme Eigenvalues of Random Matrices

Cited by in corpus (2)

• Support vector machines and linear regression coincide with very high-dimensional features
• Intersection probabilities and kinematic formulas for polyhedral cones