Difference between an eigenspace and an eigenvector ?

sid9221 · Apr 30, 2012

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.

Fredrik · Apr 30, 2012

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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Difference between an eigenspace and an eigenvector ?

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