Camille Jordan
Encyclopedia
Marie Ennemond Camille Jordan (January 5, 1838 – January 22, 1922) was a French
mathematician
, known both for his foundational work in group theory
and for his influential Cours d'analyse. He was born in Lyon
and educated at the École polytechnique
. He was an engineer by profession; later in life he taught at the École polytechnique and the Collège de France
, where he had a reputation for eccentric choices of notation.
He is remembered now by name in a number of foundational results:
Jordan's work did much to bring Galois theory
into the mainstream. He also investigated the Mathieu group
s, the first examples of sporadic group
s. His Traité des substitutions, on permutation group
s, was published in 1870.
The asteroid
25593 Camillejordan
and Institute of Camille Jordan are named in his honour.
Camille Jordan is not to be confused with the geodesist Wilhelm Jordan (Gauss-Jordan elimination) or the physicist Pascual Jordan
(Jordan algebra
s).
France
The French Republic , The French Republic , The French Republic , (commonly known as France , is a unitary semi-presidential republic in Western Europe with several overseas territories and islands located on other continents and in the Indian, Pacific, and Atlantic oceans. Metropolitan France...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
, known both for his foundational work in group theory
Group theory
In mathematics and abstract algebra, group theory studies the algebraic structures known as groups.The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces can all be seen as groups endowed with additional operations and...
and for his influential Cours d'analyse. He was born in Lyon
Lyon
Lyon , is a city in east-central France in the Rhône-Alpes region, situated between Paris and Marseille. Lyon is located at from Paris, from Marseille, from Geneva, from Turin, and from Barcelona. The residents of the city are called Lyonnais....
and educated at the École polytechnique
École Polytechnique
The École Polytechnique is a state-run institution of higher education and research in Palaiseau, Essonne, France, near Paris. Polytechnique is renowned for its four year undergraduate/graduate Master's program...
. He was an engineer by profession; later in life he taught at the École polytechnique and the Collège de France
Collège de France
The Collège de France is a higher education and research establishment located in Paris, France, in the 5th arrondissement, or Latin Quarter, across the street from the historical campus of La Sorbonne at the intersection of Rue Saint-Jacques and Rue des Écoles...
, where he had a reputation for eccentric choices of notation.
He is remembered now by name in a number of foundational results:
- The Jordan curve theoremJordan curve theoremIn topology, a Jordan curve is a non-self-intersecting continuous loop in the plane, and another name for a Jordan curve is a "simple closed curve"...
, a topological result required in complex analysisComplex analysisComplex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is useful in many branches of mathematics, including number theory and applied mathematics; as well as in physics,... - The Jordan normal formJordan normal formIn linear algebra, a Jordan normal form of a linear operator on a finite-dimensional vector space is an upper triangular matrix of a particular form called Jordan matrix, representing the operator on some basis...
and the Jordan matrixJordan matrixIn the mathematical discipline of matrix theory, a Jordan block over a ring R is a matrix composed of 0 elements everywhere except for the diagonal, which is filled with a fixed element \lambda\in R, and for the superdiagonal, which is composed of ones...
in linear algebraLinear algebraLinear algebra is a branch of mathematics that studies vector spaces, also called linear spaces, along with linear functions that input one vector and output another. Such functions are called linear maps and can be represented by matrices if a basis is given. Thus matrix theory is often... - In mathematical analysisMathematical analysisMathematical analysis, which mathematicians refer to simply as analysis, has its beginnings in the rigorous formulation of infinitesimal calculus. It is a branch of pure mathematics that includes the theories of differentiation, integration and measure, limits, infinite series, and analytic functions...
, Jordan measureJordan measureIn mathematics, the Peano–Jordan measure is an extension of the notion of size to shapes more complicated than, for example, a triangle, disk, or parallelepiped....
(or Jordan content) is an area measure that predates measure theory. - In group theoryGroup theoryIn mathematics and abstract algebra, group theory studies the algebraic structures known as groups.The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces can all be seen as groups endowed with additional operations and...
the Jordan-Hölder theorem on composition seriesComposition seriesIn abstract algebra, a composition series provides a way to break up an algebraic structure, such as a group or a module, into simple pieces. The need for considering composition series in the context of modules arises from the fact that many naturally occurring modules are not semisimple, hence...
is a basic result. - Jordan's theorem on finite linear groups
Jordan's work did much to bring Galois theory
Galois theory
In mathematics, more specifically in abstract algebra, Galois theory, named after Évariste Galois, provides a connection between field theory and group theory...
into the mainstream. He also investigated the Mathieu group
Mathieu group
In the mathematical field of group theory, the Mathieu groups, named after the French mathematician Émile Léonard Mathieu, are five finite simple groups he discovered and reported in papers in 1861 and 1873; these were the first sporadic simple groups discovered...
s, the first examples of sporadic group
Sporadic group
In the mathematical field of group theory, a sporadic group is one of the 26 exceptional groups in the classification of finite simple groups. A simple group is a group G that does not have any normal subgroups except for the subgroup consisting only of the identity element, and G itself...
s. His Traité des substitutions, on permutation group
Permutation group
In mathematics, a permutation group is a group G whose elements are permutations of a given set M, and whose group operation is the composition of permutations in G ; the relationship is often written as...
s, was published in 1870.
The asteroid
Asteroid
Asteroids are a class of small Solar System bodies in orbit around the Sun. They have also been called planetoids, especially the larger ones...
25593 Camillejordan
25593 Camillejordan
25593 Camillejordan is a main belt asteroid with a perihelion of 2.003887 AU. It has an eccentricity of 0.2255882 and an orbital period of 1320.8758111 days ....
and Institute of Camille Jordan are named in his honour.
Camille Jordan is not to be confused with the geodesist Wilhelm Jordan (Gauss-Jordan elimination) or the physicist Pascual Jordan
Pascual Jordan
-Further reading:...
(Jordan algebra
Jordan algebra
In abstract algebra, a Jordan algebra is an algebra over a field whose multiplication satisfies the following axioms:# xy = yx # = x ....
s).
Books by C. Jordan
- Cours d'analyse de l'Ecole Polytechnique ; 1 Calcul différentiel (Gauthier-Villars, 1909)
- Cours d'analyse de l'Ecole Polytechnique ; 2 Calcul intégral (Gauthier-Villars, 1909)
- Cours d'analyse de l'Ecole Polytechnique ; 3 équations différentielles (Gauthier-Villars, 1909)
- Mémoire sur le nombre des valeurs des fonctions (1861–1869)
- Recherches sur les polyèdres (Gauthier-Villars, 1866)
- The collected works of Camille Jordan were published 1961–1964 in four volumes at Gauthier-Villars, Paris.
See also
- Jordan-Chevalley decompositionJordan-Chevalley decompositionIn mathematics, the Jordan–Chevalley decomposition, named after Camille Jordan and Claude Chevalley , expresses a linear operator as the sum of its commuting semisimple part and its nilpotent parts...
- Jordan totient function
- Jordan–Schur theoremJordan–Schur theoremIn mathematics, the Jordan–Schur theorem also known as Jordan's theorem on finite linear groups is a theorem in its original form due to Camille Jordan...
- Jordan–Schönflies theorem
- Jordan's lemmaJordan's lemmaIn complex analysis, Jordan's lemma is a result frequently used in conjunction with the residue theorem to evaluate contour integrals and improper integrals...