Question

I have a general question regarding eigenvalues/vectors. Say you are working on a matrix [ 1, 1; 4, 1] and you find the eigenvalues to be 3 and -1.
Does it matter which eigenvalue is first...meaning does it matter when it is lambda_1= 3 and lambda_2=-1 or vice versa.

Answer 1

It does not matter the order in which the eigenvalues are listed

Answer 2

The order doesn't matter-what matters is the eigenvector associated with the eigenvalue. They are not exchangeable!