2018/07/12 by Paul Breiding, Breiding, Paul, Khazhgali Kozhasov +3
Computer Science · Mathematics · #Topological and Geometric Data Analysis #Advanced Combinatorial Mathematics #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.1807.04530
We investigate some geometric properties of the real algebraic variety\n\Δ of symmetric matrices with repeated eigenvalues. We explicitly compute\nthe volume of its intersection with the sphere and prove a\nEckart-Young-Mirsky-type theorem for the distance function from a generic\nmatrix to points in \Δ. We exhibit connections of our study to Real\nAlgebraic Geometry (computing the Euclidean Distance Degree of \Δ) and\nRandom Matrix Theory.\n