Abstract

A matrix seminorm ∥·∥ is called supspectral if it satisfies the condition that the spectral radius of a square matrix A is lim sup ∥ A n ∥ 1/ n as n→∞. This property is shown to be equivalent to each of two conditions on ∥·∥, one characterizing behavior on idempotent A, and the other characterizing behavior on non-nilpotent A. Examples of supspectral seminorms are provided.

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