Self-adjoint Matrices are Equivariant

2017/01/24 by Michael Dellnitz, Dellnitz, Michael
Computer Science · Mathematics · Physics and Astronomy · #15A24 #15B57 #37G40 #41A58 #Advanced Optimization Algorithms Research #FOS: Mathematics #General Mathematics (math.GM) #Matrix Theory and Algorithms #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.1701.07020

openalex publication_date 2017/01/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this short note we prove that a matrix A∈ℝ^n,n is self-adjoint if and only if it is equivariant with respect to the action of a group Γ⊂ \bf O(n) which is isomorphic to ⊗_k=1ⁿZ₂. Moreover we discuss potential applications of this result, and we use it in particular for the approximation of higher order derivatives for smooth real valued functions of several variables.

Related

• Equivariant spaces of matrices of constant rank
• On determining the domain of the adjoint operator
• Some notes about matrices, 5
• Eigenvectors From Eigenvalues: The Case of One-Dimensional Schr "odinger\n Operators
• Equivariant spaces of matrices of constant corank one