- Let A be an (nxn) matrix such that A^2 = 0 [A squared equals to the (nxn) zero matrix] Prove that if A^2 = 0 (zero matrix), then 0 is the only eigenvalue of A.
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Let $\lambda$ be an eigenvalue of A, and let $\mathbf{v}$ be the corresponding eigenvector, such that $A\mathbf{v} = \lambda\mathbf{v}$. Show more…
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