# Generalized Perron Roots and Solvability of the Absolute Value Equation

@article{Radons2019GeneralizedPR, title={Generalized Perron Roots and Solvability of the Absolute Value Equation}, author={Manuel Radons}, journal={ArXiv}, year={2019}, volume={abs/1912.08157} }

Let $A$ be a real $(n\times n)$-matrix. The piecewise linear equation system $z-A\vert z\vert =b$ is called an absolute value equation (AVE). It is well known to be uniquely solvable for all $b\in\mathbb R^n$ if and only if a quantity called the sign-real spectral radius of $A$ is smaller than one. We construct a similar quantity that we call the aligning spectral radius $\rho^a$ of $A$. We prove that the AVE is solvable for all $b\in\mathbb R^n$ if the aligning spectral radius of $A$ is…

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