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Classification des matrices entières non négatives de petites normes. (Classification of non-negative integral matrices with small norms). (French) Zbl 0624.15013

We classify matrices with non-negative integer coefficients having norms (as bounded operators) smaller than 2.0198. In particular matrices of norms smaller than 2 which are indecomposable in the appropriate sense are classified by Coxeter diagrams of type A,D,E. There are applications to semi-simple subalgebras of complex semi-simple algebras.

MSC:

15A60 Norms of matrices, numerical range, applications of functional analysis to matrix theory
47L30 Abstract operator algebras on Hilbert spaces
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