Thread: Math Q&A Game
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Apr13-05, 06:32 PM
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Hurkyl's Avatar
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If a matrix A is diagonalizable, then I claim that there exists an n such that all of the nonzero eigenvalues of An lie in the right half-plane. The requirement that Tr(An) = 0, forces all the eigenvalues to be 0, and thus A is zero... clearly nilpotent!

So the trick, then, is when the matrix is not diagonalizable.

Then again, this only works for complex valued matrices.