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  • The Mathematics of Frobenius in Context: A Journey Through 18th to 20th Century Mathematics (1st Edition)

The Mathematics of Frobenius in Context: A Journey Through 18th to 20th Century Mathematics (1st Edition)

1st Edition
Book Info
Year: 2013
Pages: 699
Language: English
Series: English
DOI: 10.1007/978-1-4614-6333-7
ISBN: 9781461463320,9781461463337

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