The Mathematics of Frobenius in Context: A Journey Through 18th to 20th Century MathematicsSpringer Science & Business Media, 23 de jul. 2013 - 699 pàgines 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. |
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The Mathematics of Frobenius in Context: A Journey Through 18th to 20th ... Thomas Hawkins Previsualització no disponible - 2013 |
The Mathematics of Frobenius in Context: A Journey Through 18th to 20th ... Thomas Hawkins Previsualització no disponible - 2015 |
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abelian functions abelian groups abelian integrals abelian matrices applied arithmetic Berlin bilinear forms canonical form Cartan Cauchy Cauchy’s Cayley’s characteristic polynomial characteristic roots Clebsch coefficients complex multiplication conjugacy classes considered corresponding Dedekind defined definition denote developed diagonal differential equations Dirichlet elementary divisors elements equivalent exist expressed finite groups follows Frobenius Galois Gauss group characters group determinant Hermite Hermite’s hypercomplex hypercomplex numbers ideal implies integral invariant factors Jacobi Jacobian Jacobian functions Kronecker Kronecker’s Kummer Lemma linear transformations mathematical mathematicians matrix algebra Molien nonnegative nonsingular normal form notation obtained orthogonal paper period matrix permutation Perron’s Pfaffian Poincar´e prime problem of Pfaff proof proved published quadratic forms rank rational realized relation representation Riemann satisfying Schur Section showed skew-symmetric solution Stickelberger subgroup symmetric theorem theory of elementary theory of group theta functions unimodular variables vector Weierstrass