arXiv 1807.045302018-07-17math.AGmath.DG

On the geometry of the set of symmetric matrices with repeated eigenvalues

Paul Breiding, Khazhgali Kozhasov, Antonio Lerario

英文摘要：

We investigate some geometric properties of the real algebraic variety $Δ$ of symmetric matrices with repeated eigenvalues. We explicitly compute the volume of its intersection with the sphere and prove a Eckart-Young-Mirsky-type theorem for the distance function from a generic matrix to points in $Δ$. We exhibit connections of our study to Real Algebraic Geometry (computing the Euclidean Distance Degree of $Δ$) and Random Matrix Theory.

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