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

• 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

• Cauchy-Frobenius Lemma (with Augustin Louis Cauchy)

• Frobenius Group
• Frobenius-Schur Indicator (with Issai Schur) (otherwise known as Schur Indicator)

• Frobenius-Stickelberger Formulas (with Ludwig Stickelberger)
• Frobenius-Stickelberger Theorem (with Ludwig Stickelberger)

• Frobenius Coin Problem
• Frobenius Number

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)

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): Entry: Frobenius, Ferdinand Georg (1849-1917)