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.
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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 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. (en)
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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 Rn × n, and a spectrahedron is a shape that can be formed by intersecting this cone with a . Spectrahedra are the feasible regions of semidefinite programs. The images of spectrahedra under linear or affine transformations are called projected spectrahedra or spectrahedral shadows. Every spectrahedral shadow is a convex set that is also semialgebraic, but the converse (conjectured to be true until 2017) is false. 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. (en)
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