MHB Invariance of Asymmetry under Orthogonal Transformation

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Orthogonal similarity transformation refers to a linear transformation that preserves angles and distances, typically represented by orthogonal matrices. The discussion emphasizes that the property of asymmetry remains unchanged when subjected to such transformations. Participants explore the mathematical proof of this invariance, highlighting the role of eigenvalues and eigenvectors in maintaining asymmetry. The conversation also touches on the implications of this property in various mathematical and physical contexts. Understanding orthogonal similarity transformations is crucial for grasping the concept of asymmetry invariance.
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Show that the property of asymmetry is invariant under orthogonal similarity transformation
 
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Okay, what IS an "orthogonal similarity transformation"? What is its definition? That's where I would start.
 

Thread 'Confusion about the Moyal-Weyl twist'

I am studying the mathematical formalism behind non-commutative geometry approach to quantum gravity. I was reading about Hopf algebras and their Drinfeld twist with a specific example of the Moyal-Weyl twist defined as F=exp(-iλ/2θ^(μν)∂_μ⊗∂_ν) where λ is a constant parametar and θ antisymmetric constant tensor. {∂_μ} is the basis of the tangent vector space over the underlying spacetime Now, from my understanding the enveloping algebra which appears in the definition of the Hopf algebra...
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