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In order to find eigenvalues we subtract the identity matrix times lambda, take the determinant of that matrix, then factor the polynomial equation to find the values of lambda. When arranging these lambda values in a diagonalized matrix, is there a rule for the which eigenvalue goes in a specific place in the diagonal or does it not matter?
No! The critical issue is that you order the eigenvalues and eigenvectors consistently. Thus, if 2 is an eigenvalue and you place it in position 3 in your order, then the corresponding eigenvector must be the third eigenvector.
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