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Sequence of spaces in linear algebra
In mathematics, particularly in linear algebra, a flag is an increasing sequence of subspaces of a finite-dimensional vector space V. Here "increasing"
Flag_(linear_algebra)
Technique in graph theory
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
Flag_algebra
Aspect of geometry
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)
Flag_(geometry)
Subgroup of the group of invertible n×n matrices
In mathematics, a linear algebraic group is a subgroup of the group of invertible n × n {\displaystyle n\times n} matrices (under matrix multiplication)
Linear_algebraic_group
Algebraic structure in linear algebra
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
Vector_space
Topics referred to by the same term
polytope Flag (linear algebra), an increasing sequence of subspaces of a vector space Flag, a baton used in the sporting event Beach Flags Flag, a type of
Flag_(disambiguation)
Type of mathematical space
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
Generalized_flag_variety
Type of subgroup of an algebraic group
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
Borel_subgroup
Special kind of square matrix
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
Triangular_matrix
Concept in mathematics
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
Reductive_group
248-dimensional exceptional simple Lie group
several closely related exceptional simple Lie groups, linear algebraic groups or Lie algebras of dimension 248; the same notation is used for the corresponding
E8_(mathematics)
{\overline {\mathbb {F} }}} is the algebraic closure of F {\displaystyle \mathbb {F} } . For the general linear Lie algebra g = g l n ( F ) {\displaystyle
Parabolic_Lie_algebra
Mathematical term
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
Bruhat_decomposition
conjecture Algebraic geometry and analytic geometry Mirror symmetry Linear algebraic group Additive group Multiplicative group Algebraic torus Reductive
List of algebraic geometry topics
List_of_algebraic_geometry_topics
Subgroup of a root system's isometry group
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
Weyl_group
Subspace preserved by a linear mapping
theorem of algebra, every linear operator on a nonzero finite-dimensional complex vector space has an eigenvector. Therefore, every such linear operator
Invariant_subspace
Theorem representing a solvable Lie algebra
{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
Lie's_theorem
Matrix factorisation in mathematics
In linear algebra, the Schur decomposition or Schur triangulation, named after Issai Schur, is a matrix decomposition. It allows one to write an arbitrary
Schur_decomposition
This is a glossary of algebraic geometry. See also glossary of commutative algebra, glossary of classical algebraic geometry, and glossary of ring theory
Glossary of algebraic geometry
Glossary_of_algebraic_geometry
Module over a sheaf of differential operators
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
D-module
and algebraic geometry, the Beilinson–Bernstein localization theorem relates D-modules on flag varieties G/B to representations of the Lie algebra g {\displaystyle
Beilinson–Bernstein localization
Beilinson–Bernstein_localization
Lie algebra, usually infinite-dimensional
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
Kac–Moody_algebra
theorem (linear algebra) Bregman–Minc inequality (discrete mathematics) Cauchy-Binet formula (linear algebra) Cayley–Hamilton theorem (Linear algebra) Dimension
List_of_theorems
Matrix decomposition method
In linear algebra, the Cholesky decomposition or Cholesky factorization (pronounced /ʃəˈlɛski/ shə-LES-kee) is a decomposition of a Hermitian, positive-definite
Cholesky_decomposition
Mathematical group of loops in a Lie group
Kac–Moody algebras and positive-energy representations. In algebraic geometry, algebraic loop groups give rise to affine Grassmannians and affine flag varieties
Loop_group
Mathematical concept in algebra
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} .
Nilpotent_matrix
induced representation of G on the group algebra over a field of G. 2. A regular representation of a linear algebraic group G is the induced representation
Glossary of representation theory
Glossary_of_representation_theory
Mathematical description of fermions
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
Dirac_spinor
On Schubert's enumerative calculus
Grassmannian defined by conditions of incidence of a linear subspace in projective space with a given flag. For details see Schubert variety. According to
Hilbert's_fifteenth_problem
In algebraic combinatorics, the h-vector of a simplicial polytope is a fundamental invariant of the polytope which encodes the number of faces of different
H-vector
Basic result in the representation theory of Lie groups
complex Lie group is one for which the corresponding Lie algebra representation is complex linear.) The weight λ gives rise to a character (one-dimensional
Borel–Weil–Bott_theorem
Mathematical structure
Tits as a means to understand the structure of isotropic reductive linear algebraic groups over arbitrary fields. The more specialized theory of Bruhat–Tits
Building_(mathematics)
Objects in representation theory of Lie algebras
operators over flag manifolds. We can explain the idea of a Verma module as follows. Let g {\displaystyle {\mathfrak {g}}} be a semisimple Lie algebra (over C
Verma_module
contrast, the analytic approach is to define projective space based on linear algebra and utilizing homogeneous co-ordinates. The propositions of incidence
Incidence_(geometry)
Theorem in Lie representation theory
theorem states that a finite-dimensional Lie algebra g {\displaystyle {\mathfrak {g}}} is a nilpotent Lie algebra if and only if for each X ∈ g {\displaystyle
Engel's_theorem
Manifold with inversion symmetry
Hermitian symmetric space gives rise to a 3-graded Lie algebra with a period 2 conjugate linear automorphism switching the parts of degree ±1 and preserving
Hermitian_symmetric_space
Swiss mathematician (1923–2003)
He worked in algebraic topology, in the theory of Lie groups, and was one of the creators of the contemporary theory of linear algebraic groups. He studied
Armand_Borel
Completion of the usual space with "points at infinity"
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
Projective_space
Russian-American mathematician
Beilinson published a paper on coherent sheaves and several problems in linear algebra. His two-page note in the journal Functional Analysis and Its Applications
Alexander_Beilinson
Geometry with 7 points and 7 lines
take any line to any other line. The Fano plane can be constructed via linear algebra as the projective plane over the finite field with two elements. One
Fano_plane
Group of symmetries of a regular polygon
geometry and abstract algebra. In geometry, Dn or Dihn refers to the symmetries of the n-gon, a group of order 2n. In abstract algebra, D2n refers to this
Dihedral_group
Rust software and development tools
learning framework for Rust ndarray — array and linear algebra operations nalgebra — general-purpose linear algebra library Polars — DataFrame library for data
List of Rust software and tools
List_of_Rust_software_and_tools
continue. The operations are typically matrix-vector products, and solving linear systems. Due to stalled upstream development, ARPACK has been forked into
ARPACK
Language theory
of context-free grammars in that nonterminals are equipped with lists of flags, or index symbols. The language produced by an indexed grammar is called
Indexed_grammar
Theoretical object in mathematics
abstract properties. This allows the development of commutative algebra and algebraic geometry on new foundations. One of the defining features of theories
Field_with_one_element
English mathematician
bundle of an algebraic variety and generalized Jacobians of linear systems’. Ann. Mat. Pura Appl. (4) 56 (1961) 359–373. ‘A problem in linear inequalities’
Aubrey_William_Ingleton
Orthogonal group of an indefinite quadratic form
Lester, J. A. (1993). "Orthochronous subgroups of O(p,q)". Linear and Multilinear Algebra. 36 (2): 111–113. doi:10.1080/03081089308818280. Zbl 0799.20041
Indefinite_orthogonal_group
Set on which a group acts freely and transitively
principal homogeneous space. One way to follow basis-dependence in a linear algebra argument is to track variables x in X. Similarly, the space of orthonormal
Principal_homogeneous_space
Construction in order theory
example, suppose P {\displaystyle P} and Q {\displaystyle Q} are the Boolean algebra on two elements. Then P ∗ Q {\displaystyle P*Q} is the poset with the Hasse
Star_product
More advanced functionality such as linear algebra is usually provided in 3rd party libraries, such as a linear algebra library or vector maths library.
Math_library
Concept in mathematics
invertible sheaf or a line bundle is also called a linearization. Let X be a complete variety over an algebraically closed field acted by a connected reductive
Equivariant_sheaf
Mathematical group that can be generated as the set of powers of a single element
In abstract algebra, a cyclic group or monogenous group is a group, denoted Cn (also frequently Z {\displaystyle \mathbb {Z} } n or Zn, not to be confused
Cyclic_group
Array representation in computer memory
reused in a computation). For example, the Basic Linear Algebra Subprograms functions are passed flags indicating which arrays are transposed. The concept
Row-_and_column-major_order
Italian mathematician
Italian mathematician, born in Florence, Italy. His main interest is algebraic geometry. Vezzosi earned an MS degree in Physics at the University of
Gabriele_Vezzosi
Classifies holomorphic vector bundles over the complex projective line
Flags, and Harmonic Maps". Mathematische Annalen. 277 (2): 249–266. doi:10.1007/BF01457363. S2CID 120270501. Roman Bezrukavnikov. 18.725 Algebraic Geometry
Birkhoff–Grothendieck_theorem
Unix-like systems. KCalc, Linux based scientific calculator Maxima: a computer algebra system which bignum integers are directly inherited from its implementation
List of arbitrary-precision arithmetic software
List_of_arbitrary-precision_arithmetic_software
Algebro-geometric stability condition
differential and algebraic geometry, K-stability is an algebro-geometric stability condition, for complex manifolds and complex algebraic varieties. The
K-stability
Six-pointed star polygon
Karamanids and Jandarids used the star on their flag. The symbol is also used on the Hayreddin Barbarossa flag. Today the six-pointed star can be found in
Hexagram
Algebraic variety in a projective space
In algebraic geometry, a projective variety is an algebraic variety that is a closed subvariety of a projective space. That is, it is the zero-locus in
Projective_variety
Digit transferred from one column to another
Hegland, M.; Wheeler, W. W. (January 1997), "Linear Bijections and the Fast Fourier Transform", Applicable Algebra in Engineering, Communication and Computing
Carry_(arithmetic)
Branch of algebraic geometry
Grassmannian defined by conditions of incidence of a linear subspace in projective space with a given flag. For further details see Schubert variety. The intersection
Schubert_calculus
expert in numerical linear algebra, founded AWM essay contest Susan Howson (born 1973), British mathematician known for work on algebraic number theory and
List_of_women_in_mathematics
In algebraic geometry, standard monomial theory describes the sections of a line bundle over a generalized flag variety or Schubert variety of a reductive
Standard_monomial_theory
Mathematical space
manifold that parameterizes the set of all k {\displaystyle k} -dimensional linear subspaces of an n {\displaystyle n} -dimensional vector space V {\displaystyle
Grassmannian
Generalisation of a sheaf; a fibered category that admits effective descent
{\displaystyle G} is a linearly reductive algebraic group. This was recently proved to be the case: given a quasi-separated algebraic stack X {\displaystyle
Stack_(mathematics)
finite-dimensional vector space V together with a subgroup G of the general linear group GL(V) such that G has an open dense orbit in V. The term prehomogeneous
Prehomogeneous_vector_space
Field of mathematics which studies incidence structures
collinear. An affine plane is a linear space satisfying: For any point A and line l not incident with it (an anti-flag) there is exactly one line m incident
Incidence_geometry
Shayman, are subvarieties of the full flag variety that are defined in terms of a Hessenberg function h and a linear transformation X. The study of Hessenberg
Hessenberg_variety
Method for dividing a simplicial complex
is an important tool in algebraic topology. The barycentric subdivision is an operation on simplicial complexes. In algebraic topology it is sometimes
Barycentric_subdivision
Type of mathematical generalization
which recovers combinatorics as linear algebra over the field with one element: for example, Weyl groups are simple algebraic groups over the field with one
Q-analog
Circle containing four or more spokes
Christians Cross – Geometrical figure Direct sum – Algebraic structure formed from a collection of algebraic structures Earth symbol – Astronomical symbols
Sun_cross
Method for finding minimum spanning trees
Jeremy; Gilbert, John (2011), Graph Algorithms in the Language of Linear Algebra, Software, Environments, and Tools, vol. 22, Society for Industrial
Prim's_algorithm
Monk's formula gives the product of a linear Schubert polynomial and a Schubert polynomial. nil-Coxeter algebra Bernstein, I. N.; Gelfand, I. M.; Gelfand
Schubert_polynomial
Ninth letter of the Latin alphabet
Boyd, Stephen; Vandenberghe, Lieven (2018). Introduction to Applied Linear Algebra: Vectors, Matrices, and Least Squares. Cambridge University Press. p
I
Concept in algebraic geometry
In algebraic geometry, a line bundle on a projective variety is nef if it has nonnegative degree on every curve in the variety. The classes of nef line
Nef_line_bundle
Harvey White B&W series of films (30m each) 1957 titles (incomplete): Algebra and Powers of Ten / The Atmosphere / Atomic Accelerators / The Bohr Atom
List of Encyclopædia Britannica Films titles
List_of_Encyclopædia_Britannica_Films_titles
Geometry without using coordinates
made by many other fields. For example, college studies now include linear algebra, topology, and graph theory where the subject is developed from first
Synthetic_geometry
2025 Android mobile operating system
and measuring text vertically. A new flag, VERTICAL_TEXT_FLAG, has been added to the Paint class. When this flag is set, Paint's text measurement APIs
Android_16
Theorem in abstract algebra
important reductions made by Jean-Loup Waldspurger to the case of Lie algebras. Time magazine placed Ngô's proof on the list of the "Top 10 scientific
Fundamental lemma (Langlands program)
Fundamental_lemma_(Langlands_program)
Distance function
principle to rederive the Perron–Frobenius theorem in finite-dimensional linear algebra and its analogues for integral operators with positive kernels. Birkhoff's
Hilbert_metric
Type of topological space
class: it is the free Z / 2 Z {\displaystyle \mathbf {Z} /2\mathbf {Z} } -algebra on w 1 {\displaystyle w_{1}} , which has degree 1. Its cohomology ring
Real_projective_space
23 mathematical problems stated in 1900
Quadratic forms with any algebraic numerical coefficients. Extensions of Kronecker's theorem on Abelian fields to any algebraic realm of rationality. Impossibility
Hilbert's_problems
Study of complex manifolds and several complex variables
concerned with the study of spaces such as complex manifolds and complex algebraic varieties, functions of several complex variables, and holomorphic constructions
Complex_geometry
Generalised concept of incidence structure of polygons
SIAM Journal on Algebraic and Discrete Methods. 5 (3): 287–293. doi:10.1137/0605030. hdl:10338.dmlcz/102386. Nozaki, Hiroshi (2014). "Linear programming bounds
Generalized_polygon
German mathematician (1906–2000)
mathematical physics, who laid important mathematical groundwork for algebraic geometry and for string theory. Erich Kähler was born in Leipzig, the
Erich_Kähler
British-Lebanese mathematician (1929–2019)
functions for linear partial differential equations can often be found by using the Fourier transform to convert this into an algebraic problem. Atiyah
Michael_Atiyah
Combinitorics of Polyhedra
their facets are available. Abstract polytope Combinatorial commutative algebra Matroid polytope Order polytope Simplicial sphere Stable matching polytope
Polyhedral_combinatorics
Day and boarding school in Dulles, Fairfax / Loudoun, Virginia, United States
students study English and English literature, the sciences, mathematics (linear algebra through Calculus BC), foreign language (French, Spanish, Latin and Chinese)
Fairfax_Christian_School
Theorem in functional analysis
In linear algebra and functional analysis, the min-max theorem, or variational theorem, or Courant–Fischer–Weyl min-max principle, is a result that gives
Min-max_theorem
General-purpose programming language
arrays are commonly used in numerical algorithms (mainly from applied linear algebra) to store matrices. The structure of the C array is well suited to this
C_(programming_language)
2023 Android mobile operating system
restrictions introduced in newer versions. An Android Debug Bridge (ADB) install flag has been added to bypass the restriction. To improve privacy, the user can
Android_14
Graph drawing used to study Riemann surfaces
by dessins are precisely those that can be defined as algebraic curves over the field of algebraic numbers. The absolute Galois group transforms these particular
Dessin_d'enfant
Programmable scientific calculator produced by Hewlett-Packard
"Celebrating 35 years". The HP 35s uses either Reverse Polish Notation (RPN) or algebraic infix notation as input. Other features of the HP 35s include: Two-line
HP_35s
Computational problem of graph theory
algebraic path problem. Most of the classic shortest-path algorithms (and new ones) can be formulated as solving linear systems over such algebraic structures
Shortest_path_problem
Numerical calculations carrying along derivatives
In mathematics and computer algebra, automatic differentiation (auto-differentiation, autodiff, or AD), also called algorithmic differentiation, computational
Automatic_differentiation
Web browser developed by Google
features. Originally called about:labs, the address was changed to about:flags to make it less obvious to casual users. The desktop edition of Chrome can
Google_Chrome
Video-sharing platform
separate HBO (for base plan subscribers) and HBO Max (for all subscribers) linear/VOD add-ons into a single combined Max offering. On February 28, 2017, in
YouTube
the line set. The dual of a linear geometry is obtained by interchanging the roles of points and lines. A survey of linear topological geometries is given
Topological_geometry
dimensions of linear subspaces, and the type map takes a linear subspace to its dimension. A flag in this case is a chain of subspaces, and each flag is contained
Buekenhout_geometry
Solving symbolic inequations
1016/S0747-7171(89)80017-3. Comon, Hubert (1990). "Equational Formulas in Order-Sorted Algebras". Proc. ICALP. Comon shows that the first-order logic theory of equality
Dis-unification
FLAG LINEAR-ALGEBRA
FLAG LINEAR-ALGEBRA
Female
Scottish
Feminine form of Scottish Gaelic Teà rlach, TEÀRLAG means "instigator."
Girl/Female
Australian, Hindu, Indian
Flag
Boy/Male
Bengali, Hindu, Indian, Marathi
Flag
Surname or Lastname
English (East Anglia) and Jewish (Ashkenazic)
English (East Anglia) and Jewish (Ashkenazic) : metonymic occupational name for someone who grew, sold, or treated flax for weaving into linen cloth, from (respectively) Middle English flax, German Flachs.
Boy/Male
Hindu
Lingam
Male
English
Irish Anglicized form of Gaelic Fionnbarr, FINBAR means "fair-headed."
Surname or Lastname
English
English : variant of Lingard.French : occupational name for a maker of or dealer in linen goods, from Old French linge ‘linen (goods)’ (see Linge 1).
Girl/Female
Hindu, Indian
A Flag
Male
Greek
(ΑἰνÎας) Variant spelling of Greek AineÃas, AINEAS means "praiseworthy."
Boy/Male
Hindu, Indian
Till End
Female
Scottish
Variant spelling of Scottish Lilias, LILEAS means "lily."
Boy/Male
Indian
Flag
Boy/Male
Indian
Flag
Female
English
Variant spelling of English Linsey, LINSAY means "Lincoln's wetlands."
Surname or Lastname
English
English : habitational name from places such as Flagg in Derbyshire and Flags in Nottinghamshire, named from Old English flage or Old Norse flaga ‘slab’, or from Old Norse flag ‘turf’, ‘sod’.
Boy/Male
Arabic, Iranian
Flag Holder
Girl/Female
Bengali, Hindu, Indian, Marathi, Sanskrit, Traditional
Flag
Male
Yiddish
 Variant spelling of Yiddish Lieber, LIBER means "beloved." Compare with another form of Liber.
Boy/Male
Arabic
Flag Holder
Boy/Male
British, English
From the Flax Field
FLAG LINEAR-ALGEBRA
FLAG LINEAR-ALGEBRA
Girl/Female
Indian, Telugu
Kind of Things
Male
Norwegian
Modern Norwegian form of Old Norse StÃgandr, STIAN means "wanderer."
Male
Scottish
Scottish Gaelic form of Greek Ioseph (Latin Josephus), IÃ’SEPH means "(God) shall add (another son)."Â
Boy/Male
Indian, Sikh
Lord of Chanting Hymns
Boy/Male
Tamil
Lord Ganesh
Boy/Male
Arabic, Muslim
Father of Mankind
Boy/Male
Hindu, Indian
Poet; Saint; Unity; Union
Boy/Male
Hindu
Well spoken of, Praiseworthy, Celebrated
Boy/Male
Tamil
Ramanuj | ராமாநà¯à®œ
Born after Rama i.e. Lakshman (Younger brother of Rama)
Boy/Male
Hindu, Indian
Betrayer
FLAG LINEAR-ALGEBRA
FLAG LINEAR-ALGEBRA
FLAG LINEAR-ALGEBRA
FLAG LINEAR-ALGEBRA
FLAG LINEAR-ALGEBRA
v. i.
To droop; to grow spiritless; to lose vigor; to languish; as, the spirits flag; the streugth flags.
v. t.
To convey, as a message, by means of flag signals; as, to flag an order to troops or vessels at a distance.
v. t.
To lay with flags of flat stones.
a.
Like a line; narrow; of the same breadth throughout, except at the extremities; as, a linear leaf.
v. t.
To let droop; to suffer to fall, or let fall, into feebleness; as, to flag the wings.
a.
In the direction of a line; of or pertaining to a line; measured on, or ascertained by, a line; linear; as, lineal magnitude.
a.
Linear.
a.
Composed of lines; delineated; as, lineal designs.
n.
Flax; linen.
n.
The longer and finer fiber of flax.
v. t.
To furnish or deck out with flags.
n.
One who lines, as, a liner of shoes.
n.
A flat stone used for paving.
a.
Of a linear shape.
a.
Of or pertaining to a line; consisting of lines; in a straight direction; lineal.
n.
That which flags or hangs down loosely.
n.
A cloth usually bearing a device or devices and used to indicate nationality, party, etc., or to give or ask information; -- commonly attached to a staff to be waved by the wind; a standard; a banner; an ensign; the colors; as, the national flag; a military or a naval flag.
v. t.
To signal to with a flag; as, to flag a train.
a.
Descending in a direct line from an ancestor; hereditary; derived from ancestors; -- opposed to collateral; as, a lineal descent or a lineal descendant.
adv.
In a linear manner; with lines.