Real Symmetric Matrices with Partitioned Eigenvalues
Algebraic Geometry
2021-10-13 v2 Representation Theory
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 give a parametrization by rational functions. For small matrices, we provide equations; for larger matrices, we explain how to use representation theory to find equations. We describe the ring of invariants under the action of the orthogonal group. For the subvariety of diagonal matrices, we give the degree.
Cite
@article{arxiv.2008.08554,
title = {Real Symmetric Matrices with Partitioned Eigenvalues},
author = {Madeleine Weinstein},
journal= {arXiv preprint arXiv:2008.08554},
year = {2021}
}
Comments
9 pages