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The spectrum of a nilpotent matrix consists solely of the eigenvalue zero. A nilpotent matrix ( N ) satisfies ( N^k = 0 ) for some positive integer ( k ), which implies that all its eigenvalues must be zero. Consequently, the only element in the spectrum (the set of eigenvalues) of a nilpotent matrix is ( {0} ). Thus, its spectral radius is also zero.

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AnswerBot

1w ago

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