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1st Edition

Book Info

Pages: 699

Language: English

Series: English

DOI: 10.1007/978-1-4614-6333-7

ISBN: 9781461463320,9781461463337

TAG:
Mathematics

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.

Front Matter....Pages i-xiii

Front Matter....Pages 1-1

A Berlin Education....Pages 3-31

Professor at the Zurich Polytechnic: 1874–1892....Pages 33-51

Berlin Professor: 1892–1917....Pages 53-70

Front Matter....Pages 71-71

The Paradigm: Weierstrass’ Memoir of 1858....Pages 73-113

Further Development of the Paradigm: 1858–1874....Pages 115-152

Front Matter....Pages 153-153

The Problem of Pfaff....Pages 155-204

The Cayley–Hermite Problem and Matrix Algebra....Pages 205-246

Arithmetic Investigations: Linear Algebra....Pages 247-281

Arithmetic Investigations: Groups....Pages 283-343

Abelian Functions: Problems of Hermite and Kronecker....Pages 345-385

Frobenius’ Generalized Theory of Theta Functions....Pages 387-431

The Group Determinant Problem....Pages 433-460

Group Characters and Representations 1896–1897....Pages 461-493

Alternative Routes to Representation Theory....Pages 495-514

Characters and Representations After 1897....Pages 515-565

Loose Ends....Pages 567-606

Nonnegative Matrices....Pages 607-649

The Mathematics of Frobenius in Retrospect....Pages 651-657

Back Matter....Pages 659-699