Difference between an eigenspace and an eigenvector ?

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SUMMARY

An eigenspace is defined as the subspace spanned by all eigenvectors corresponding to a specific eigenvalue. In the context of a rotation matrix R around the z-axis in ℝ3, the vectors (0,0,1), (0,0,2), and (0,0,-1) serve as eigenvectors with the eigenvalue of 1. The eigenspace corresponding to this eigenvalue is identified as the z-axis. This distinction clarifies that an eigenspace is not a type of eigenvector, but rather a collection of eigenvectors associated with a particular eigenvalue.

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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.
 

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