Let A be a real symmetric matriz that σ(A) = {0}. Prove that A=O
This exercise is for orthogonal diagonalization. How do I apply the spectrum theorem to get this proof?
2026-04-04 01:01:51.1775264511
I don't understand what this question mean, but I need to prove it for homework
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Hints:
=== A matrix has zero as its unique eigenvalue (in any extension of the base field) iff it is nilpotent
=== A symmetric matrix is always diagonalizable (over the reals)
=== The only nilpotent diagonalizable matrix is the zero one.