Goodman, Fred; de la Harpe, Pierre; Jones, Vaughan Classification des matrices entières non négatives de petites normes. (Classification of non-negative integral matrices with small norms). (French) Zbl 0624.15013 C. R. Acad. Sci., Paris, Sér. I 300, 463-465 (1985). 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 Keywords:classification; non-negative integral matrices with small norms; bounded operators; Coxeter diagrams; semi-simple algebras PDFBibTeX XMLCite \textit{F. Goodman} et al., C. R. Acad. Sci., Paris, Sér. I 300, 463--465 (1985; Zbl 0624.15013)