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Important information about eigenvectors and eigenvalues

Let V be the set of real valued sequences {see attachment}.

? Check that V is a vector space over the field of real numbers, using addition of vectors {see attachment} and scalar multiplication {see attachment}.

Let T be the linear shift map sending {see attachment}.

? Check that T is a linear transformation and compute its eigenvalues and eigenvectors.


Solution Summary

Eigenvectors and Eigenvalues problems are solved. The solution is detailed and well presented.