Ferdinand Georg Frobenius
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Ferdinand Georg Frobenius , called Georg, (born October 26, 1849 in Berlin , † August 3, 1917 in Charlottenburg , today a district of Berlin) was a German mathematician .
Life
Georg Frobenius was the son of the teacher Christian Ferdinand Frobenius and Christiane Elisabeth Friedrich. From 1860 he attended the Joachimsthalsche Gymnasium in Berlin-Charlottenburg and in 1867 studied first one semester at the Georg-August-Universität Göttingen , then at the Friedrich-Wilhelms-Universität Berlin and received his doctorate there in 1870 under Karl Weierstrass and Ernst Eduard Kummer . First he taught at the Sophiengymnasium in Berlin . In 1874 he was appointed associate professor at the University of Berlin, without ever having completed his habilitation . Just one year later, he accepted an appointment at the Swiss Federal Polytechnic in Zurich . In 1892 he returned to the University of Berlin as the successor to the late Leopold Kronecker . There he set high standards for exams.
Together with Leopold Kronecker, Lazarus Immanuel Fuchs and Hermann Amandus Schwarz , he belonged to the inner circle of famous Berlin mathematicians of his time. He was also a member of the Prussian Academy of Sciences . In 1889 he was elected a member of the Leopoldina .
He married Augusta Sophia Lehmann on April 19, 1876 in Berlin (* May 28, 1852 Berlin, daughter of the headmaster Martin Friedrich and Maria Charlotta Dannenberg, † March 29, 1903 Berlin)
plant
Frobenius was mainly concerned with the theory of groups and their representation theory .
Various mathematical terms are named after him, including:
- Frobenius group
- Frobenius homomorphism in commutative algebra
- Frobenius manifolds
- Frobenius matrix
- Frobenius norm
- Frobenius normal form for endomorphisms of finite-dimensional vector spaces
- Frobenius problem
- Frobenius reciprocity
- Frobenius dot product
- Frobenius number
- Frobenius theorem (differential topology)
- Frobenius theorem (real division algebras)
In 1878 Frobenius proved Cayley-Hamilton's theorem for matrices of any dimension. In 1877 he proved Frobenius' theorem that there are only three associative finite-dimensional division algebras over the real numbers, the real numbers themselves, the complex numbers and the quaternions .
literature
- Nikolaus Stuloff: Frobenius, Ferdinand Georg. In: New German Biography (NDB). Volume 5, Duncker & Humblot, Berlin 1961, ISBN 3-428-00186-9 , p. 641 ( digitized version ).
- Jean-Pierre Serre (editor): Frobenius, Gesammelte Abhandlungen, 3 volumes, Springer Verlag 1968, reprint 2015
- Thomas W. Hawkins : The mathematics of Frobenius in context. A journey through 18th to 20th century mathematics. Springer, New York 2013
See also
Web links
- Literature by and about Ferdinand Georg Frobenius in the catalog of the German National Library
- John J. O'Connor, Edmund F. Robertson : Ferdinand Georg Frobenius. In: MacTutor History of Mathematics archive .
Individual evidence
- ↑ Frobenius, On linear substitutions and bilinear forms, J. Reine Angew. Math., Volume 84, 1877, pp. 1-63, SUB Göttingen , reprinted in Frobenius, Gesammelte Abhandlungen, Volume 1, pp. 343-405
| personal data | |
|---|---|
| SURNAME | Frobenius, Ferdinand Georg |
| ALTERNATIVE NAMES | Frobenius, Georg |
| BRIEF DESCRIPTION | German mathematician |
| DATE OF BIRTH | October 26, 1849 |
| PLACE OF BIRTH | Charlottenburg , Germany |
| DATE OF DEATH | August 3, 1917 |
| Place of death | Berlin , Germany |