Publications
Preprint · arXiv · March 29, 2021
On eigenvalues of symmetric matrices with PSD principal submatrices
Abstract
We investigate convexity properties of the set of eigenvalue tuples of $n\times n$ real symmetric matrices, whose all $k\times k$ (where $k\leq n$ is fixed) minors are positive semidefinite. It is proven that the set $λ(\mathcal{S}^{n,k})$ of eigenvalue vectors of all such matrices is star-shaped with respect to the nonnegative orthant $\mathbb{R}^n_{\geq 0}$ and not convex already when $(n,k)=(4,2)$.
Matrix Theory and AlgorithmsMathematical Inequalities and ApplicationsAdvanced Optimization Algorithms Researchreal symmetric matricesconvexitystar-shaped sets
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