Relationship between inverse matrix and inertia tensor?

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The discussion explores the relationship between the inverse of a matrix and the inertia tensor, suggesting a potential connection. Participants question whether this relationship is valid and inquire about the determinant of the matrix in question. The inertia tensor, a key concept in physics, is often represented in matrix form, leading to speculation about its inverse properties. The conversation highlights the importance of understanding these mathematical relationships in the context of mechanics. Overall, the thread emphasizes the need for further clarification on the determinant and its implications for the inertia tensor.
Bruno Tolentino
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Seems exist some relationship between the inverse of a matrix with the inertia tensor, looks:

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This relationship really exist?
 
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What's the determinant of that matrix?
 
I think that we knows what's...
 
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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