Difference between an eigenspace and an eigenvector ?

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An eigenspace is not a special type of eigenvector; rather, it is the subspace formed by all eigenvectors associated with a specific eigenvalue. For instance, in the case of a rotation around the z-axis in ℝ3, the eigenvectors (0,0,1), (0,0,2), and (0,0,-1) all share the eigenvalue of 1. The eigenspace corresponding to this eigenvalue is represented by the z-axis. Understanding this distinction clarifies the relationship between eigenvectors and eigenspaces in linear algebra. This foundational concept is crucial for grasping more advanced topics in the field.
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So I'm a bit confused between these two and can't quite find any useful resources online. So is an eigenspace a special type of eigenvector cause that's how I understand it now.
 
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No, an eigenspace is the subspace spanned by all the eigenvectors with the given eigenvalue. For example, if R is a rotation around the z axis in ℝ3, then (0,0,1), (0,0,2) and (0,0,-1) are examples of eigenvectors with eigenvalue 1, and the eigenspace corresponding to eigenvalue 1 is the z axis.
 
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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