eigenvalues and eigenvectors (different solution between matlab and book) Could you please help me to solve this?

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!!

Answer 1

[David Goodmanson]

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.

[Emmanuel Vidales]

Thank you!!. You right. I missed that simple detail. I really appreciate your help. Nice day!