Spectrahedron (original) (raw)

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 Rn × n, and a spectrahedron is a shape that can be formed by intersecting this cone with a . An example of a spectrahedron is the spectraplex, defined as where is the set of n × n positive semidefinite matrices and is the trace of the matrix . The spectraplex is a compact set, and can be thought of as the "semidefinite" analog of the simplex.