Marie Ennemond Camille Jordan (; 5 January 1838 – 22 January 1922) was a French mathematician, known both for his foundational work in
group theory
In abstract algebra, group theory studies the algebraic structures known as group (mathematics), groups.
The concept of a group is central to abstract algebra: other well-known algebraic structures, such as ring (mathematics), rings, field ...
and for his influential ''Cours d'analyse''.
Biography
Jordan was born in
Lyon
Lyon,, ; Occitan: ''Lion'', hist. ''Lionés'' also spelled in English as Lyons, is the third-largest city and second-largest metropolitan area of France. It is located at the confluence of the rivers Rhône and Saône, to the northwest of t ...
and educated at the
École polytechnique
École may refer to:
* an elementary school in the French educational stages normally followed by secondary education establishments (collège and lycée)
* École (river), a tributary of the Seine flowing in région Île-de-France
* École, Savoi ...
. He was an engineer by profession; later in life he taught at the École polytechnique and the
Collège de France
The Collège de France (), formerly known as the ''Collège Royal'' or as the ''Collège impérial'' founded in 1530 by François I, is a higher education and research establishment (''grand établissement'') in France. It is located in Paris ne ...
, where he had a reputation for eccentric choices of notation.
He is remembered now by name in a number of results:
* The
Jordan curve theorem
In topology, the Jordan curve theorem asserts that every ''Jordan curve'' (a plane simple closed curve) divides the plane into an " interior" region bounded by the curve and an "exterior" region containing all of the nearby and far away exterior ...
, a topological result required in
complex analysis
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates Function (mathematics), functions of complex numbers. It is helpful in many branches of mathemati ...
* The
Jordan normal form
In linear algebra, a Jordan normal form, also known as a Jordan canonical form (JCF),
is an upper triangular matrix of a particular form called a Jordan matrix representing a linear operator on a finite-dimensional vector space with respect to som ...
and the
Jordan matrix
In the mathematical discipline of matrix theory, a Jordan matrix, named after Camille Jordan, is a block diagonal matrix over a ring (whose identities are the zero 0 and one 1), where each block along the diagonal, called a Jordan block, has the ...
in
linear algebra
Linear algebra is the branch of mathematics concerning linear equations such as:
:a_1x_1+\cdots +a_nx_n=b,
linear maps such as:
:(x_1, \ldots, x_n) \mapsto a_1x_1+\cdots +a_nx_n,
and their representations in vector spaces and through matrices.
...
* In
mathematical analysis
Analysis is the branch of mathematics dealing with continuous functions, limit (mathematics), limits, and related theories, such as Derivative, differentiation, Integral, integration, measure (mathematics), measure, infinite sequences, series (m ...
,
Jordan measure In mathematics, the Peano–Jordan measure (also known as the Jordan content) is an extension of the notion of size ( length, area, volume) to shapes more complicated than, for example, a triangle, disk, or parallelepiped.
It turns out that for ...
(or ''Jordan content'') is an area measure that predates
measure theory
In mathematics, the concept of a measure is a generalization and formalization of geometrical measures ( length, area, volume) and other common notions, such as mass and probability of events. These seemingly distinct concepts have many simil ...
* In
group theory
In abstract algebra, group theory studies the algebraic structures known as group (mathematics), groups.
The concept of a group is central to abstract algebra: other well-known algebraic structures, such as ring (mathematics), rings, field ...
, the
Jordan–Hölder theorem on composition series is a basic result.
*
Jordan's theorem on finite linear groups
Jordan's work did much to bring
Galois theory
In mathematics, Galois theory, originally introduced by Évariste Galois, provides a connection between field theory and group theory. This connection, the fundamental theorem of Galois theory, allows reducing certain problems in field theory to ...
into the mainstream. He also investigated the
Mathieu group
In group theory, a topic in abstract algebra, the Mathieu groups are the five sporadic simple groups ''M''11, ''M''12, ''M''22, ''M''23 and ''M''24 introduced by . They are multiply transitive permutation groups on 11, 12, 22, 23 or 24 objec ...
s, the first examples of
sporadic group
In mathematics, a sporadic group is one of the 26 exceptional groups found in the classification of finite simple groups.
A simple group is a group ''G'' that does not have any normal subgroups except for the trivial group and ''G'' itself. The ...
s. His ''Traité des substitutions'', on
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'' (which are thought of as bijective functions from the set ''M'' to it ...
s, was published in 1870; this treatise won for Jordan the 1870
''prix Poncelet''. He was an Invited Speaker of the
ICM in 1920 in
Strasbourg
Strasbourg (, , ; german: Straßburg ; gsw, label=Bas Rhin Alsatian, Strossburi , gsw, label=Haut Rhin Alsatian, Strossburig ) is the prefecture and largest city of the Grand Est region of eastern France and the official seat of the Eu ...
.
The
asteroid
An asteroid is a minor planet of the inner Solar System. Sizes and shapes of asteroids vary significantly, ranging from 1-meter rocks to a dwarf planet almost 1000 km in diameter; they are rocky, metallic or icy bodies with no atmosphere.
...
25593 Camillejordan and are named in his honour.
Camille Jordan is not to be confused with the
geodesist
Geodesy ( ) is the Earth science of accurately measuring and understanding Earth's figure (geometric shape and size), orientation in space, and gravity. The field also incorporates studies of how these properties change over time and equivale ...
Wilhelm Jordan Wilhelm Jordan may refer to:
* Carl Friedrich Wilhelm Jordan (1819–1904), known as Wilhelm Jordan, German writer and politician
* Wilhelm Jordan (geodesist) (1842–1899), German scientist, noted for the Gauss–Jordan elimination algorithm
{{hn ...
(
Gauss–Jordan elimination
In mathematics, Gaussian elimination, also known as row reduction, is an algorithm for solving systems of linear equations. It consists of a sequence of operations performed on the corresponding matrix of coefficients. This method can also be used ...
) or the physicist
Pascual Jordan
Ernst Pascual Jordan (; 18 October 1902 – 31 July 1980) was a German theoretical and mathematical physicist who made significant contributions to quantum mechanics and quantum field theory. He contributed much to the mathematical form of matrix ...
(
Jordan algebra
In abstract algebra, a Jordan algebra is a nonassociative algebra over a field whose multiplication satisfies the following axioms:
# xy = yx (commutative law)
# (xy)(xx) = x(y(xx)) ().
The product of two elements ''x'' and ''y'' in a Jordan al ...
s).
Bibliography
* 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
*
Centered tree
In the mathematical subfield of graph theory, a centered tree is a tree with only one center, and a bicentered tree is a tree with two centers.
Given a graph, the eccentricity of a vertex is defined as the greatest distance from to any othe ...
*
Frenet–Serret formulas
In differential geometry, the Frenet–Serret formulas describe the kinematic properties of a particle moving along a differentiable curve in three-dimensional Euclidean space \mathbb^, or the geometric properties of the curve itself irrespective ...
*
Pochhammer contour
In mathematics, the Pochhammer contour, introduced by Jordan (1887), pp. 243–244 and , is a contour in the complex plane with two points removed, used for contour integration. If ''A'' and ''B'' are loops around the two points, both starting a ...
References
External links
*
*
{{DEFAULTSORT:Jordan, Camille
1838 births
1922 deaths
École Polytechnique alumni
Mines Paris - PSL alumni
Corps des mines
Scientists from Lyon
19th-century French mathematicians
Group theorists
Linear algebraists
Academic staff of the Collège de France
Corresponding members of the Saint Petersburg Academy of Sciences
Members of the French Academy of Sciences
Foreign Members of the Royal Society
Foreign associates of the National Academy of Sciences
Members of the Ligue de la patrie française