Publications
Article · Arnold Mathematical Journal · December 19, 2018
On the Geometry of the Set of Symmetric Matrices with Repeated Eigenvalues
Paul Breiding, Khazhgali Kozhasov, Antonio Lerario
Abstract
Abstract We investigate some geometric properties of the real algebraic variety $$\Delta $$ 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 $$\Delta $$ Δ . We exhibit connections of our study to real algebraic geometry (computing the Euclidean distance degree of $$\Delta $$ Δ ) and random matrix theory.
Matrix Theory and AlgorithmsAdvanced Combinatorial MathematicsPolynomial and algebraic computationsymmetric matricesrepeated eigenvaluesreal algebraic varieties
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