Title The mathematics of Frobenius in context : a journey through 18th to 20th Century mathematics / Thomas Hawkins

Published New York : Springer, ©2013

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Description 1 online resource (698 pages) Series Sources and Studies in the History of Mathematics and Physical Sciences Sources and studies in the history of mathematics and physical sciences. Contents Overview of Frobenius' Career and Mathematics. A Berlin Education -- Professor at the Zurich Polytechnic: 1874-1892 -- Berlin Professor: 1892-1917 -- Berlin-Style Linear Algebra. The Paradigm: Weierstrass' Memoir of 1858 -- Further Development of the Paradigm: 1858-1874 -- The Mathematics of Frobenius. The Problem of Pfaff -- The Cayley-Hermite Problem and Matrix Algebra -- Arithmetic Investigations: Linear Algebra -- Arithmetic Investigations: Groups -- Abelian Functions: Problems of Hermite and Kronecker -- Frobenius' Generalized Theory of Theta Functions -- The Group Determinant Problem -- Group Characters and Representations 1896-1897 -- Alternative Routes to Representation Theory -- Characters and Representations After 1897 -- Loose Ends -- Nonnegative Matrices -- The Mathematics of Frobenius in Retrospect Summary Frobenius made many important contributions to mathematics in the latter part of the 19th century. Hawkins here focuses on his work in linear algebra and its relationship with the work of Burnside, Cartan, and Molien, and its extension by Schur and Brauer. He also discusses the Berlin school of mathematics and the guiding force of Weierstrass in that school, as well as the fundamental work of d'Alembert, Lagrange, and Laplace, and of Gauss, Eisenstein and Cayley that laid the groundwork for Frobenius's work in linear algebra. The book concludes with a discussion of Frobenius's contribution to the theory of stochastic matrices Bibliography Includes bibliographical references and index Notes English Print version record In Springer eBooks Subject Frobenius, Ferdinand Georg, 1849-1917. SUBJECT Frobenius, Ferdinand Georg, 1849-1917 fast Subject Algebras, Linear -- History Mathematics -- History MATHEMATICS -- Algebra -- Intermediate. Álgebra lineal -- Historia Matemáticas -- Historia Algebras, Linear Mathematics Genre/Form History Form Electronic book LC no. 2013941038 ISBN 9781461463337 1461463335 1461463327 9781461463320 9781299859098 1299859097

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