# Elliptope

This arises in semi-definite programming. It is the set of all real, square symmetric matrices whose diagonal entries are all equal to one and whose eigenvalues are all non-negative. The dimension of the set is $LaTeX: n(n-1)/2$ (where the matrix is $LaTeX: n \times n$). For example, consider $LaTeX: n=2$:
$LaTeX: M = \left[ \begin{array}{cc} 1 & a \\ a & 1 \end{array} \right]$.
Then, $LaTeX: M$ is in the elliptope for $LaTeX: n=2$ if, and only if, $LaTeX: -1 \le a \le 1$, i.e. it is diagonally dominate (note the dimension is 1). An elliptope is also called a set of correlation matrices.