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In convex geometry, a spectrahedron is a shape that can be represented as a linear matrix inequality. Alternatively, the set of n × n positive semidefinite matrices forms a convex cone in R, and a spectrahedron is a shape that can be formed by intersecting this cone with a linear affine subspace.
Spectrahedra are the solution spaces of semidefinite programs.
References
- Ramana, Motakuri; Goldman, A. J. (1995), "Some geometric results in semidefinite programming", Journal of Global Optimization, 7 (1): 33–50, doi:10.1007/BF01100204.
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