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 .
• 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.