Mathematician:Ferdinand Georg Frobenius

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's Theorem

• Frobenius Endomorphism
• Frobenius Group
• Frobenius Number

• 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)

• Frobenius Coin Problem
• Frobenius-Stickelberger Theorem (with Ludwig Stickelberger)

• Cauchy-Frobenius Lemma (with Augustin Louis Cauchy)

• 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

• Ruelle-Perron-Frobenius Theorem (with David Pierre Ruelle and Oskar Perron)

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