# Mathematician:Ferdinand Georg Frobenius

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## Mathematician

German mathematician best known for his work on differential equations and group theory.

Gave the first full proof of the Cayley-Hamilton Theorem.

## Nationality

German

## History

- Born: 26 Oct 1849 in Berlin-Charlottenburg, Prussia (now Germany)
- Died: 3 Aug 1917 in Berlin, Germany

## Theorems and Definitions

- Frobenius-Schur Indicator (with Issai Schur) (otherwise known as Schur Indicator)
- Frobenius-Stickelberger Formulas (with Ludwig Stickelberger)

- Ruelle-Perron-Frobenius Operator (with David Pierre Ruelle and Oskar Perron) (also known as the Ruelle operator)

- Rouché-Frobenius Theorem (with Eugène Rouché) (although Frobenius merely discussed the result; priority actually goes to Georges Fontené): also known as:

- Rouché-Fontené Theorem (after Eugène Rouché and Georges Fontené) as it is known in France
- Rouché-Capelli Theorem (after Eugène Rouché and Alfredo Capelli) as it is known in Italy
- Kronecker-Capelli Theorem (after Leopold Kronecker and Alfredo Capelli) as it is known in Russia

Results named for **Ferdinand Georg Frobenius** can be found here.

Definitions of concepts named for **Ferdinand Georg Frobenius** can be found here.

## Publications

- 1878:
*Über lineare Substitutionen und bilineare Formen*(*J. reine angew. Math.***Vol. 84**: pp. 1 – 63)

- 1897:
*Über die Darstellung der endlichen Gruppen durch lineare Substitutionen*(*Sitzungsber., Preuss. Akad. Wiss.***Vol. 1897**: pp. 994 – 1015)

## Also known as

Some sources report his name as **Georg Ferdinand Frobenius**.

## Sources

- John J. O'Connor and Edmund F. Robertson: "Ferdinand Georg Frobenius": MacTutor History of Mathematics archive

- 1989: Ephraim J. Borowski and Jonathan M. Borwein:
*Dictionary of Mathematics*... (previous) ... (next):**Frobenius, Ferdinand Georg**(1849-1917) - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**Frobenius's theorem** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**Frobenius's theorem**