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 one year ago
Let V be vector space with dim(V)=n and T:V>V a linear operator. If y is an eigenvalue of T with geometric multiplicity n, then show that every nonzero vector of V is an eigenvector.
I have no idea how to prove. I think I have to use the definition of Eigenvalues and Eigenvectors of Linear Operators but not sure how.
 one year ago
Let V be vector space with dim(V)=n and T:V>V a linear operator. If y is an eigenvalue of T with geometric multiplicity n, then show that every nonzero vector of V is an eigenvector. I have no idea how to prove. I think I have to use the definition of Eigenvalues and Eigenvectors of Linear Operators but not sure how.

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