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Results tagged with eigenvalues
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user 81488
eigenvalues of matrices or operators
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Lower eigenvectors of nonnegative matrices with zero trace
Let $\lambda_1,\ldots, \lambda_N$ be its eigenvalues ordered in the decreasing order with respect to their real parts, and $v_1,\ldots, v_N$ be the corresponding (left) eigenvectors. … Perron and Frobenius tell us that $\lambda_1$ is a strictly positive real number and therefore (since the sum of eigenvalues must be zero) there must also be eigenvalues with strictly negative real part …
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