On the finiteness property for rational matrices
By Raphaël M. Jungers, Vincent D. Blondel. 2007
52 citations recorded by the source corpus.
In this chapter we analyze a recent conjecture stating that the finiteness property holds for pairs of binary matrices. We show that the finiteness property holds for all pairs of binary matrices if and only if it holds for all sets of nonnegative rationalmatrices.We provide a similar result for matrices with positive and negative entries. We finally prove the conjecture for 2×2 matrices.
Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Electrical and Electronic Engineering
View Paper: https://www.semanticscholar.org/paper/b72aab81744a21f7abc808585a5043de8d7e4aa8
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In Algebra and Number Theory
In Computational Theory and Mathematics
In Electrical and Electronic Engineering
Citations in the corpus
- Continuity properties of the lower spectral radius (2013, background): “Whilst Lagarias and Wang’s conjecture was subsequently shown to be false [19], it is believed that the upper finiteness property holds for typical finite sets of matrices in various senses [21, 36, 42] and this question continues to stimulate research [10, 22, 32, 46].”
- Mather sets for sequences of matrices and applications to the study of joint spectral radii (2011, background): “Mairesse [13], but continues to stimulate research [7, 14, 25, 30, 33, 38].”