Ergodicity Coefficients Defined by Vector Norms
SIAM Journal on Matrix Analysis and Applications
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A nonlinear matrix iterative process is a linear dynamical system for which there is a nonlinear feedback of the current vector on the entries of the matrix. Stability conditions for an asymptotically exponential solution are studied for such a process in the positive quadrant of $\mathbb{R}^{n}.$ The results hinge on a generalization of the coefficient of ergodicity of a nonnegative matrix.