MATLAB: Eigenvalues and eigenvectors (different solution between matlab and book) Could you please help me to solve this

eigenvalueseigenvectorslinsolveMATLAB

Hello,
I can't to figure out how to match the results between my book and matlab, I really appreciate if you help me to understand this topic.
My book:
But when I use Matlab the solutions are these:
The eigenvalues are matched, but eigenvectors are different.
If I try to solve through linsolve function when I equal the function to zero, this happens:
I don't know what is my mistake.
Thank you!!

Best Answer

Hi Emmanuel,
Eigenvectors are not defined uniquely, in the sense that if v is an eigenvector of M, then any nonzero constant times v is also an eigenvector of M. In your case for eigenvalue 0, the book eigenvector is [2; -1] and the Matlab eigenvector is V(:,1) = [-.8944; .4472]. These differ only by an overall multiplicative constant. Similarly for eigenvalue 5, [1; 2] and [.4472; .8944] differ only by an overall multiplicative constant. It's necessary to make a definite choice and Matlab defines its eigenvectors so that norm(eigenvector) = 1 but this is not a requirement.
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