Isotropy groups of the action of orthogonal similarity on symmetric matrices

2021/08/15 by Tadej Starčič, Starčič, Tadej · 2 citations
Computer Science · Mathematics · #Algebraic and Geometric Analysis #Differential Geometry (math.DG) #FOS: Mathematics #Matrix Theory and Algorithms #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2108.06757

openalex publication_date 2021/08/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We find an algorithmic procedure that enables to compute and to describe the structure of the isotropy subgroups of the group of complex orthogonal matrices with respect to the action of similarity on complex symmetric matrices. A key step in our proof is to solve a certain rectangular block upper-triangular Toeplitz matrix equation.

Cited by

• Isotropy groups of the action of orthogonal similarity on skew-symmetric and on complex orthogonal matrices
• Algebraic versions of \mathbbT² and of ℙ¹×ℙ¹ and Hochschild cohomology

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