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arXiv · 2103.15811

On eigenvalues of symmetric matrices with PSD principal submatrices

Khazhgali Kozhasov
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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 $\lambda(\mathcal{S}^{n,k})$ 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 $(n,k)=(4,2)$.

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Khazhgali Kozhasov. 2021-03-29. On eigenvalues of symmetric matrices with PSD principal submatrices. https://arxiv.org/abs/2103.15811

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