Bounds via spectral radius-preserving row sum expansions

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Joseph P. Stover


We show a simple method for constructing larger dimension nonnegative matrices with somewhat arbitrary entries which can be irreducible or reducible but preserving the spectral radius via row sum expansions. This yields a sufficient criteria for two square nonnegative matrices of arbitrary dimension to have the same spectral radius, a way to compare spectral radii of two arbitrary square nonnegative matrices, and a way to derive new upper and lower bounds on the spectral radius which give the standard row sum bounds as a special case.

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