why fourth Option is not the right answer ? And can invariance be generalized to more than one dimensional subspace? I think third option is correct.
2026-03-30 00:04:02.1774829042
Invariance under linear transformation
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You're right that the third option is correct. The fourth can't be since if there were two different eigenvalues the sum of their eigenvectors couldn't also be an eigenvector.
That argument should suggest a generalization.