For the Perron roots of square nonnegative matrices A,B, and A + D-1BTD, where D is a diagonal matrix with positive diagonal entries, the inequality ρ(A + D-1BTD) ≥ ρ(A) + ρ(B) is proved under the assumption that A and B ...

Let p(t) be a monic polynomial. We obtain two bounds for zeros of p(t) via the Perron root and the numerical radius of the companion matrix of the polynomial.