In mathematics, particularly in linear algebra, a flag is an increasing sequence of subspaces of a finite-dimensional vector space V. Here "increasing"...

inserting suitable subspaces. According to basic results of linear algebra, any two complete flags in an n-dimensional vector space V over a field F are no...

polyhedron or higher polytope Flag (linear algebra), an increasing sequence of subspaces of a vector space Flagstone or flag, a large flat stone used for...

In mathematics, a linear algebraic group is a subgroup of the group of invertible n × n {\displaystyle n\times n} matrices (under matrix multiplication)...

Flag algebras are an important computational tool in the field of graph theory which have a wide range of applications in homomorphism density and related...

but also a direction. The concept of vector spaces is fundamental for linear algebra, together with the concept of matrices, which allows computing in vector...

matrix Tridiagonal matrix Invariant subspace Axler, Sheldon Jay (1997). Linear Algebra Done Right (2nd ed.). New York: Springer. pp. 86–87, 169. ISBN 0-387-22595-1...

a reductive group is a type of linear algebraic group over a field. One definition is that a connected linear algebraic group G over a perfect field is...

ISBN 0-8218-0288-7. J. Humphreys (1972). Linear Algebraic Groups. New York: Springer. ISBN 0-387-90108-6. Milne, J. S. (2017), Algebraic Groups: The Theory of Group...

conjecture Algebraic geometry and analytic geometry Mirror symmetry Linear algebraic group Additive group Multiplicative group Algebraic torus Reductive...

{gl}}(V)} is a finite-dimensional representation of a solvable Lie algebra, then there is a flag V = V 0 ⊃ V 1 ⊃ ⋯ ⊃ V n = 0 {\displaystyle V=V_{0}\supset V_{1}\supset...

several closely related exceptional simple Lie groups, linear algebraic groups or Lie algebras of dimension 248; the same notation is used for the corresponding...

In the mathematical discipline of linear algebra, the Schur decomposition or Schur triangulation, named after Issai Schur, is a matrix decomposition. It...

theorem of algebra, every linear operator on a nonzero finite-dimensional complex vector space has an eigenvector. Therefore, every such linear operator...

above as well as the related flag concept from linear algebra. A flag is maximal if it is not contained in a larger flag. An incidence geometry (Ω, I)...

This is a glossary of algebraic geometry. See also glossary of commutative algebra, glossary of classical algebraic geometry, and glossary of ring theory...

connection to flag manifolds have natural analogues in the Kac–Moody setting. A class of Kac–Moody algebras called affine Lie algebras is of particular...

decomposition for affine groups. Cluster algebra This Week's Finds in Mathematical Physics, Week 186 Borel, Armand. Linear Algebraic Groups (2nd ed.). New York: Springer-Verlag...

In linear algebra, a matrix is in row echelon form if it can be obtained as the result of Gaussian elimination. Every matrix can be put in row echelon...

a semisimple Lie algebra, a semisimple linear algebraic group, etc. is the Weyl group of the root system of that group or algebra. Let Φ {\displaystyle...

In linear algebra, a nilpotent matrix is a square matrix N such that N k = 0 {\displaystyle N^{k}=0\,} for some positive integer k {\displaystyle k} ....

{\overline {\mathbb {F} }}} is the algebraic closure of F {\displaystyle \mathbb {F} } . For the general linear Lie algebra g = g l n ( F ) {\displaystyle...

Beilinson–Bernstein localization. It relates D-modules on flag varieties G/B to representations of the Lie algebra g {\displaystyle {\mathfrak {g}}} of a reductive...

theorem (linear algebra) Bregman–Minc inequality (discrete mathematics) Cauchy-Binet formula (linear algebra) Cayley–Hamilton theorem (Linear algebra) Dimension...

In linear algebra, the Cholesky decomposition or Cholesky factorization (pronounced /ʃəˈlɛski/ shə-LES-kee) is a decomposition of a Hermitian, positive-definite...

contrast, the analytic approach is to define projective space based on linear algebra and utilizing homogeneous co-ordinates. The propositions of incidence...

set of a Clifford algebra. Further basis elements σμν of the Clifford algebra are given by Only six of the matrices σμν are linearly independent. This...

definition, which is more often encountered in modern textbooks. Using linear algebra, a projective space of dimension n is defined as the set of the vector...

continue. The operations are typically matrix-vector products, and solving linear systems. Due to stalled upstream development, ARPAСK has been forked into...

and algebraic geometry, the Beilinson–Bernstein localization theorem relates D-modules on flag varieties G/B to representations of the Lie algebra g {\displaystyle...