Perron-Frobenius theorem

PERRON, OSKAR.

Zur Theorie der Matrices.

Leipzig, B. G. Teubner, 1907. 8vo. Bound in contemporary half calf with gilt lettering to spine. In "Mathematische Annalen", 64. Band, 1907. Hinges and extremities with wear. Bookplates to pasted down front free end-paper. Internally fine and clean. Pp. 248-263. [Entire volume: IV, 576 pp].

First printing of Perron's important paper on positive matrices which profoundly influenced several fields of science.

"Today the Perron-Frobenius mathematics of nonnegative matrices enjoys wide applications, the most sensational perhaps being its implicit use by millions of internet surfers, who routinely activate Google's PageRank algorithm every day. Such a remarkable worldwide application in an electronic search engine is a far cry from the original theoretical articles, written more than a century ago, by Perron and Frobenius. These two German scholars preferred to concentrate on pure mathematics. Especially Frobenius in Berlin considered applications as inferior subjects that should be relegated to technical schools" (PARYS, How pioneers of linear economics overlooked Perron-Frobenius mathematics).

The volume also contain Hjelmslev's important paper: "Neue Begründung der ebenen Geometrie" and Brill's paper on three-dimensional algebraic curves: "Ueber algebraische Raumkurven".

Order-nr.: 47453