Theorem 1.1 (Frobenius-Perron). Let B be an n × n matrix with nonnegative entries. Then we have the following: (1) B has a nonnegative real eigenvalue. The largest such eigenvalue, λ(B), dominates the absolute values of all other eigenvalues of B. The domination is strict if the entries of B are strictly positive. (2) If B has strictly positive entries… (More)
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