首页|Real symmetric matrices with partitioned eigenvalues

Real symmetric matrices with partitioned eigenvalues

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  • NSTL
  • Elsevier
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. (C) 2021 Elsevier Inc. All rights reserved.

Real algebraic varietyReal symmetric matricesEuclidean distance degreeDegenerate matricesDISCRIMINANT

Weinstein, Madeleine

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2022

10.1016/j.laa.2021.10.016

Linear Algebra and its Applications

Linear Algebra and its Applications

EISCI
ISSN：0024-3795
年,卷(期)：2022.633
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