specifically linear algebra, the Jordan–Chevalley decomposition, named after Camille Jordan and Claude Chevalley, expresses a linear operator in a unique...

mathematics, Jordan decomposition may refer to Hahn decomposition theorem, and the Jordan decomposition of a measure Jordan normal form of a matrix Jordan–Chevalley...

matrix polynomial, which can be computed efficiently. By the Jordan–Chevalley decomposition, any n × n {\displaystyle n\times n} matrix X with complex entries...

The Jordan–Chevalley decomposition of an element in algebraic group as a product of semisimple and unipotent elements The Bruhat decomposition G = B...

decreasing size. The Jordan–Chevalley decomposition is particularly simple with respect to a basis for which the operator takes its Jordan normal form. The...

properness Chevalley group Chevalley scheme Chevalley–Iwahori–Nagata theorem Beck–Chevalley condition Non-conformist movement Jordan–Chevalley decomposition Patrick...

the multiplicative version of the Jordan–Chevalley decomposition. There is also a version of the Jordan decomposition for groups: any commutative linear...

into a diagonalizable matrix by a small perturbation; and the Jordan–Chevalley decomposition states that any matrix is uniquely the sum of a diagonalizable...

diagonalized, the Jordan–Chevalley decomposition does this without choosing a basis. Applicable to: square matrix A Decomposition (complex version):...

Marie Ennemond Camille Jordan (French: [ʒɔʁdɑ̃]; 5 January 1838 – 22 January 1922) was a French mathematician, known both for his foundational work in...

define the Drazin inverse over any perfect field, by using the Jordan-Chevalley decomposition A = A s + A n {\displaystyle A=A_{s}+A_{n}} where A s {\displaystyle...

T}Q_{gTg^{-1},G_{s}}(u)\theta (g^{-1}sg)} where x=su is the Jordan–Chevalley decomposition of x as the product of commuting semisimple and unipotent elements...

In mathematics, the Bruhat decomposition (introduced by François Bruhat for classical groups and by Claude Chevalley in general) G = B W B {\displaystyle...

connection to divided differences. A related notion is the Jordan–Chevalley decomposition which expresses a matrix as a sum of a diagonalizable and a...

and only if it is diagonalizable. Over a perfect field, the Jordan–Chevalley decomposition expresses an endomorphism x : V → V {\displaystyle x:V\to V}...

{gl}}_{n}}(x)} also has the Jordan decomposition, which can be shown (see Jordan–Chevalley decomposition) to respect the above Jordan decomposition; i.e., ad g l n...

converse can be deduced from the nilpotency criterion based on the Jordan–Chevalley decomposition, as explained there. Applying Cartan's criterion to the adjoint...

nilpotent diagonalizable matrix is the zero matrix. See also: Jordan–Chevalley decomposition#Nilpotency criterion. Consider the n × n {\displaystyle n\times...

Jordan normal form Jordan–Chevalley decomposition — sum of commuting nilpotent matrix and diagonalizable matrix Schur decomposition — similarity transform...

Lie algebras. For example, the Jordan decomposition in a semisimple Lie algebra coincides with the Jordan decomposition in its representation; this is...

{\displaystyle \lambda _{1},\lambda _{2},\ldots ,\lambda _{k}} . The Jordan–Chevalley decomposition theorem states that A {\displaystyle A} is similar to a block...

simple Lie algebras, see the list of simple Lie groups. By means of a Chevalley basis for the Lie algebra, one can define E8 as a linear algebraic group...

{h}}_{1}} is irreducible. This decomposition of the orthogonal symmetric Lie algebra yields a direct product decomposition of the corresponding compact...

groups. The founders of the theory of algebraic groups include Maurer, Chevalley, and Kolchin (1948). In the 1950s, Armand Borel constructed much of the...

L/C_{n}(L)} Chevalley 1.  Claude Chevalley (1909 – 1984), a French mathematician 2.  A Chevalley basis is a basis constructed by Claude Chevalley with the...

theory) Doob decomposition theorem (stochastic processes) Doob's martingale convergence theorems (stochastic processes) Doob–Meyer decomposition theorem (stochastic...

{\displaystyle \mathbb {Z} _{p}} of p-adic integers. Part of Claude Chevalley's construction of the finite groups of Lie type involves showing that a...

a D with positive diagonal entries. In that case, if S in the above decomposition is positive definite, then A is said to be a Cartan matrix. The Cartan...

carry over to this setting: submodule, quotient, subquotient, direct sum, Jordan-Hölder series, etc. A simple but useful tool in studying irreducible representations...