A spectrahedron is a convex set specified by requiring an affine function of its variables
with values in real symmetric
matrices to be positive semidefinite
(Netzer and Sanyal 2015). It has the form
where the matrices 
have a common finite size. Such
sets are the feasible regions of semidefinite
programming. For example, the closed unit disk 
is described by
See also
Generalized Lax Conjecture,
Positive Semidefinite Matrix,
Semidefinite
Programming,
Spectrahedral Shadow
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References
Netzer, T. and Sanyal, R. "Smooth Hyperbolicity Cones Are Spectrahedral Shadows." Math. Program. 153, 213-221, 2015.
https://doi.org/10.1007/s10107-014-0744-6.
Cite this as:
Weisstein, Eric W. "Spectrahedron." From
MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Spectrahedron.html
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