# Ferdinand Georg Frobenius

**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

**Commons : Ferdinand Georg Frobenius**- Collection of images, videos and audio files

- 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 | |
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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 |