# 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.

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Let V be the set of real valued sequences .

â€¢ Check that V is a vector space over the field of real numbers, using addition of vetors and scalar multiplication .

(1) First we want to show the addition is closed in V

If , then both are real valued sequence, let , ...

#### Solution Summary

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