Order of Eigenvectors in Diagonalization

[blackrose75]

I essentially know how to find eigenvalues and thus eigenvectors, though when solving a problem about diagonalization I do not know how to order them (as in, I can find all the eigenvectors but do not know which order to place them into find my X that diagonalizes my A)

In the examples of my book it first seems to be the largest value (putting the eigenvector corresponding to the eigenvector 1 first then the one to -4), but when I go to another example it puts them in order of 0, 1, 1 (each being one of the eigenvalues.)

Apologies if I phrased this question confusingly, it's a bit late and my test is in another day or two.

Thanks.

 

[Deveno]

there's not "one way" to diagonalize a matrix, there's several ways, corresponding to different orderings of the eigenvalues. pick an order of the eigenvalues that works for you.