\(\DeclarePairedDelimiterX{\Set}[2]{\{}{\}}{#1 \nonscript\;\delimsize\vert\nonscript\; #2}\) \( \DeclarePairedDelimiter{\set}{\{}{\}}\) \( \DeclarePairedDelimiter{\parens}{\left(}{\right)}\) \(\DeclarePairedDelimiterX{\innerproduct}[1]{\langle}{\rangle}{#1}\) \(\newcommand{\ip}[1]{\innerproduct{#1}}\) \(\newcommand{\bmat}[1]{\left[\hspace{2.0pt}\begin{matrix}#1\end{matrix}\hspace{2.0pt}\right]}\) \(\newcommand{\barray}[1]{\left[\hspace{2.0pt}\begin{matrix}#1\end{matrix}\hspace{2.0pt}\right]}\) \(\newcommand{\mat}[1]{\begin{matrix}#1\end{matrix}}\) \(\newcommand{\pmat}[1]{\begin{pmatrix}#1\end{pmatrix}}\) \(\newcommand{\mathword}[1]{\mathop{\textup{#1}}}\)
Needs:
Real Positive Semidefinite Matrix Cone ›
Real Affine Sets ›
Needed by:
None.
Links:
Sheet PDF ›
Graph PDF ›

Real Spectrahedra

Definition

A subset $S \subset \mathbfsf{S} _{++}^n$ of the cone of positive semidefinite matrices is a spectrahedron (or real spectrahedron) if there exists an affine subset $M \subset \mathbfsf{S} _{++}^n$ so that

\[ S = \mathbfsf{S} _{++}^n \cap M \]

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