Jordan decomposition
Encyclopedia
In mathematics
, Jordan decomposition may refer to
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, Jordan decomposition may refer to
- Hahn decomposition theoremHahn decomposition theoremIn mathematics, the Hahn decomposition theorem, named after the Austrian mathematician Hans Hahn, states that given a measurable space and a signed measure μ defined on the σ-algebra Σ, there exist two sets P and N in Σ such that:...
, and the Jordan decomposition of a measure - 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...
of a matrix - Jordan–Chevalley decomposition of a matrix
- Deligne–Lusztig theoryDeligne–Lusztig theoryIn mathematics, Deligne–Lusztig theory is a way of constructing linear representations of finite groups of Lie type using ℓ-adic cohomology with compact support, introduced by ....
, and its Jordan decomposition of a character of a finite group of Lie type - The Jordan–Hölder theorem, about decompositions of finite groupFinite groupIn mathematics and abstract algebra, a finite group is a group whose underlying set G has finitely many elements. During the twentieth century, mathematicians investigated certain aspects of the theory of finite groups in great depth, especially the local theory of finite groups, and the theory of...
s.