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most citedAsymptotic behavior of the smallest eigenvalue of matrices associated with completely even functions (mod r)

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math.SP2012

Power series with positive coefficients arising from the characteristic polynomials of positive matrices

Thomas J. Laffey, Raphael Loewy, Helena Šmigoc

Let A be an nxn (entrywise) positive matrix and let f(t)=det(I-t A). We prove that there always exists a positive integer N such that 1-f(t)^{1/N} has positive coefficients.