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We study the real algebraic variety of real symmetric matrices with eigenvalue multiplicities determined by a partition. We present formulas for the dimension and Euclidean Distance Degree. We use representation… Click to show full abstract
We study the real algebraic variety of real symmetric matrices with eigenvalue multiplicities determined by a partition. We present formulas for the dimension and Euclidean Distance Degree. We use representation theory to provide a rational parametrization. For small matrices, we provide equations; for larger matrices, we explain how to find equations. We describe the ring of invariants under the action of the special orthogonal group. For the subvariety of diagonal matrices, we give the Hilbert polynomial.
Journal Title: Linear Algebra and its Applications
Year Published: 2021
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