# The finiteness conjecture for the generalized spectral radius of a set of matrices

@article{Lagarias1995TheFC,
title={The finiteness conjecture for the generalized spectral radius of a set of matrices},
author={Jeffrey C. Lagarias and Yang Wang},
journal={Linear Algebra and its Applications},
year={1995},
volume={214},
pages={17-42}
}
• Published 1995
• Mathematics
• Linear Algebra and its Applications
The generalized spectral radius\g9(∑) of a set ∑ of n × n matrices is \g9(∑) = lim supk→∞\g9k(∑)1k, where \g9k(∑) = sup{ϱ(A1A2…Ak): each Ai ∈ ∑}. The joint spectral radius\g9(∑) is \g9(∑) = lim supk→∞\g9k(∑)1k, where \g9k(∑) = sup{∥A1 … Ak∥:each Ai ∈ ∑}. It is known that \g9(∑) = \g9(∑) holds for any finite set ∑ of n × n matrices. The finiteness conjecture asserts that for any finite set ∑ of real n × n matrices there exists a finite k such that \g9(∑) = \g9(∑) = \g9k(∑)1k. The normed…
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