I have found the eigenvalue and from that I have found the eigenspaces of A. The next step is to find orthonormal eigenvectors. The problem has three different eigenspaces. When I was solving the problem I randomly picked one and let it be v1 to solve for v2 and v3. The book picked a different eigenspace, from the three, as v1. Does it matter that I didn't pick the same eigenspace as the book because it will change the order when I construct a matrix Q? We have the same values but column two and one are switched.
2026-04-08 17:27:03.1775669223
Does the order of Q matter?
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It does not matter.
You are free to choose any order you like.
Just be consistent of the placement of the eigenvalues and the eigenvectors should follow those.