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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.
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Curvature measures and Steiner formulae in space forms
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The kinematic formula in Riemannian homogeneous spaces
R. Howard · 1993
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Convex bodies: the Brunn-Minkowski theory
R. Schneider · 1993
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Analysis on symmetric cones
J. Faraut and A. Korányi · 1994
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F. Morgan · 1995
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The geometry of semidefinite programming
G. Pataki · 2000
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A mathematical view of interior-point methods in convex optimization
J. Renegar · 2001
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A course in convexity
A. Barvinok · 2002
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Self-scaled barrier functions on symmetric cones and their classification
R. A. Hauser and O. Güler · 2002
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Kinematic and Crofton formulae of integral geometry: recent variants and extensions (survey)
D. Hug and R. Schneider · 2002
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Solving linear programs with finite precision. I. Condition numbers and random programs
D. Cheung and F. Cucker · 2004
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Random fields and geometry
R. J. Adler and J. E. Taylor · 2007
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Convex and discrete geometry
P. M. Gruber · 2007
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The importance of the Selberg integral
P. J. Forrester and S. O. Warnaar · 2008
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Stochastic and integral geometry
R. Schneider and W. Weil · 2008
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A general formula for the algebraic degree in semidefinite programming
H.-C. G. v. Bothmer and K. Ranestad · 2009
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The algebraic degree of semidefinite programming
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Geometric analysis of the condition of the convex feasibility problem
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