# On the Ordering of Spectral Radius Product r(A) r(AD) Versus r(A^2 D) and Related Applications

@article{Altenberg2013OnTO, title={On the Ordering of Spectral Radius Product r(A) r(AD) Versus r(A^2 D) and Related Applications}, author={Lee Altenberg}, journal={arXiv: Spectral Theory}, year={2013} }

For a nonnegative matrix A and real diagonal matrix D, two known inequalities on the spectral radius, r(A^2 D^2) >= r(AD)^2 and r(A) r(A D^2) >= r(AD)^2, leave open the question of what determines the order of r(A^2 D^2) with respect to r(A) r(A D^2). This is a special case of a broad class of problems that arise repeatedly in ecological and evolutionary dynamics. Here, sufficient conditions are found on A that determine orders in either direction. For a diagonally symmetrizable nonnegative…

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