Matrices and spectra satisfying the Newton inequalities (original) (raw)
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Let A be a n×n entrywise nonnegative matrix and let s_k:=trace(A^k), k=1,2,3. It is shown that if n>1 then View the MathML source is nonnegative. The result is used to show that if View the MathML source is the spectrum of a nonnegative matrix where λ2 is nonreal and λ_1=max(|λ_j|,j=1,…,n) then View the MathML source need not be realizable for all t>0 even when Re(λ_2)⩾0 .