Elliptope

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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.


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