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Type of mathematical group
group is a group G consisting of invertible matrices over a specified field K, with the operation of matrix multiplication. A linear group is a group
Linear_group
Group of 𝑛 × 𝑛 invertible matrices
In mathematics, the general linear group of degree n {\displaystyle n} is the set of n × n {\displaystyle n\times n} invertible matrices, together with
General_linear_group
US musical group
Linear (pronounced: /lɪˈnɪər/; lin-EER) is an American freestyle-pop group from Fort Lauderdale, Florida. The lineup originally consisted of founder, lead
Linear_(group)
Construction in group theory
especially in the group theoretic area of algebra, the projective linear group (also known as the projective general linear group or PGL) is the induced
Projective_linear_group
Group of matrices with determinant 1
In mathematics, the special linear group SL ( n , R ) {\displaystyle \operatorname {SL} (n,R)} of degree n {\displaystyle n} over a commutative ring
Special_linear_group
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
Mathematical group
reductive linear algebraic group with values in a finite field. The important collection of finite simple groups of Lie type make up most of the groups in the
Group_of_Lie_type
Undeciphered writing system of ancient Crete
were four major branches of this group: Linear A, Linear B, Cypro-Minoan, and Cretan hieroglyphic. In the 1950s, Linear B was deciphered and its underlying
Linear_A
Group that is also a differentiable manifold with group operations that are smooth
Lie group is defined as a topological group with at most countably many connected components that is, near the identity, a linear Lie group. A linear Lie
Lie_group
Transformations induced by a mathematical group
of the group. In the case of a finite-dimensional vector space, it allows one to identify many groups with subgroups of the general linear group GL (
Group_action
Type of group in mathematics
by analogy with the general linear group. Equivalently, it is the group of n × n orthogonal matrices, where the group operation is given by matrix multiplication
Orthogonal_group
Orientation-preserving mapping class group of the torus
In mathematics, the modular group is the projective special linear group PSL ( 2 , Z ) {\displaystyle \operatorname {PSL} (2,\mathbb {Z} )} of 2 × 2
Modular_group
Set with associative invertible operation
matrix groups or linear groups. The dihedral group example mentioned above can be viewed as a (very small) matrix group. Another important matrix group is
Group_(mathematics)
Group of all affine transformations of an affine space
translations, and the affine group of A can be described concretely as the semidirect product of V by GL(V), the general linear group of V: Aff ( V ) = V ⋊
Affine_group
Algebraic variety with a group structure
orthogonal groups, general linear groups, projective groups, Euclidean groups, etc. Many matrix groups are also algebraic. Other algebraic groups occur naturally
Algebraic_group
Group of unitary complex matrices with determinant of 1
{\displaystyle \mathbb {C} ^{n}} . It is itself a subgroup of the general linear group, SU ( n ) ⊂ U ( n ) ⊂ GL ( n , C ) . {\displaystyle \operatorname
Special_unitary_group
Sum of elements on the main diagonal
In linear algebra, the trace of a square matrix A, denoted tr(A), is defined as a sum of the elements on its main diagonal, a 11 + a 22 + ⋯ + a n n {\displaystyle
Trace_(linear_algebra)
Mathematical function, in linear algebra
In mathematics, and more specifically in linear algebra, a linear map (or linear mapping) is a particular kind of function between vector spaces, which
Linear_map
Group homomorphism into the general linear group over a vector space
mathematical field of representation theory, group representations describe abstract groups in terms of bijective linear transformations of a vector space to
Group_representation
Equivalence under a change of basis (linear algebra)
linear group, the notion of conjugacy may be more restrictive than similarity, since it requires that P be chosen to lie in H. When defining a linear
Matrix_similarity
Projective line over the real numbers
projective transformations, homographies, or linear fractional transformations. They form the projective linear group PGL(2, R). Each element of PGL(2, R) can
Real_projective_line
Concept in mathematics
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
Reductive_group
Mathematical object studied in the field of algebraic geometry
A general linear group is an example of a linear algebraic group, an affine variety that has a structure of a group in such a way the group operations
Algebraic_variety
Mathematical group formed from the automorphisms of an object
automorphism group of X is the group of invertible linear transformations from X to itself (the general linear group of X). If instead X is a group, then its
Automorphism_group
Geometric transformation that preserves lines but not angles nor the origin
affine group, which has the general linear group of degree n {\displaystyle n} as subgroup and is itself a subgroup of the general linear group of degree
Affine_transformation
Branch of mathematics
Linear algebra is the branch of mathematics concerning linear equations such as a 1 x 1 + ⋯ + a n x n = b , {\displaystyle a_{1}x_{1}+\cdots +a_{n}x_{n}=b
Linear_algebra
Integral transform
3-dimensional family, and can be visualized as the action of the special linear group SL2(C) on the time–frequency plane (domain). As this defines the original
Linear canonical transformation
Linear_canonical_transformation
Subgroup of a root system's isometry group
these. The Weyl group of a semisimple Lie group, a semisimple Lie algebra, a semisimple linear algebraic group, etc. is the Weyl group of the root system
Weyl_group
Type of group in abstract algebra
theory of Coxeter groups, the symmetric group is the Coxeter group of type An and occurs as the Weyl group of the general linear group. In combinatorics
Symmetric_group
Type of group in mathematics
setting of Lie groups, this includes the real, complex, and quaternionic general linear, special linear, orthogonal, unitary, and symplectic groups, together
Classical_group
Group with translationally invariant total order
In mathematics, specifically abstract algebra, a linearly ordered or totally ordered group is a group G equipped with a total order "≤" that is translation-invariant
Linearly_ordered_group
Group of unitary matrices
unitary matrices, with the group operation of matrix multiplication. The unitary group is a subgroup of the general linear group GL ( n , C ) {\displaystyle
Unitary_group
Algebraic object with geometric applications
tensor uses the representations of the general linear group. There is an action of the general linear group on the set of all ordered bases of an n-dimensional
Tensor
Connected non-abelian Lie group lacking nontrivial connected normal subgroups
when it is isomorphic to the projective special linear group. The first classification of simple Lie groups was by Wilhelm Killing, and this work was later
Simple_Lie_group
Statistical modeling method
In statistics, linear regression is a model that estimates the relationship between a scalar response (dependent variable) and one or more explanatory
Linear_regression
Topics referred to by the same term
up linear in Wiktionary, the free dictionary. Linearity is a property of various things in mathematics, physics, and electronics. Linear, linearly, or
Linear_(disambiguation)
Commutative group (mathematics)
of linearly independent (over the integers) elements of the group. Finite abelian groups and torsion groups have rank zero, and every abelian group of
Abelian_group
Möbius transformation generalized to rings other than the complex numbers
In mathematics, a linear fractional transformation is, roughly speaking, an invertible transformation of the form z ↦ a z + b c z + d . {\displaystyle
Linear fractional transformation
Linear_fractional_transformation
list of transitive finite linear groups is an important classification of certain highly symmetric actions of finite groups on vector spaces. The solvable
List of transitive finite linear groups
List_of_transitive_finite_linear_groups
Tools for studying groups based on techniques from algebraic topology
of Linear Groups, Progress in Mathematics, vol. 193, Birkhäuser Verlag, Zbl 0997.20045 Milne, James (2013), "Chapter II: The Cohomology of Groups", Class
Group_cohomology
Mathematical group
In mathematics, the symplectic group is the group of linear transformations that preserve the geometric structure of phase space, the space of position
Symplectic_group
Result on the topology of operators on an infinite-dimensional, complex Hilbert space
maximal compact subgroup, the unitary group U of H. The proof that the complex general linear group and unitary group have the same homotopy type is by the
Kuiper's_theorem
Sporadic simple group
projective special linear group of 3-dimensional space over the finite field with 4 elements (Dixon & Mortimer 1996, pp. 192–205). This group, sometimes called
Mathieu_group_M24
Five sporadic simple groups
sporadic simple group, being isomorphic to the projective special linear group PSL(3,4). Mathieu (1861, p.271) introduced the group M12 as part of an
Mathieu_group
Branch of mathematics that studies abstract algebraic structures
studies abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studies modules over these abstract
Representation_theory
Archaeological horizon of Neolithic Europe
from the German Linearbandkeramik, it is also known as the Linear Band Ware, Linear Ware, Linear Ceramics or Incised Ware culture, falling within the Danubian I
Linear_Pottery_culture
Conjectures connecting number theory and geometry
groups is trivial. Langlands generalized the idea of functoriality: instead of using the general linear group GL(n), other connected reductive groups
Langlands_program
Universal construction of a complex Lie group from a real Lie group
original group. They are isomorphic if the original group has a quotient by a discrete normal subgroup which is linear. For compact Lie groups, the complexification
Complexification_(Lie_group)
Mathematical group with trivial abelianization
perfect group need not be simple; for example, the special linear group over the field with 5 elements, SL(2,5) (or the binary icosahedral group, which
Perfect_group
Structure group sub-bundle on a tangent frame bundle
For example, for the orthogonal group, an O(n)-structure defines a Riemannian metric, and for the special linear group an SL(n,R)-structure is the same
G-structure_on_a_manifold
Mathematical study of invariants under symmetries
under the transformations from a given linear group. For example, if we consider the action of the special linear group SLn on the space of n by n matrices
Invariant_theory
Branch of mathematics that studies the properties of groups
theory have influenced many parts of algebra. Linear algebraic groups and Lie groups are two branches of group theory that have experienced advances and have
Group_theory
Rational function of the form (az + b)/(cz + d)
the complex projective line. They form a group called the Möbius group, which is the projective linear group PGL(2, C). Together with its subgroups, it
Möbius_transformation
Integer matrices with +1 or −1 determinant; invertible over the integers. GL_n(Z)
integer solution. The n × n unimodular matrices form a group called the n × n general linear group over Z {\displaystyle \mathbb {Z} } , which is denoted
Unimodular_matrix
1990 single by Linear
"Sending All My Love" is a song by American freestyle/pop group Linear from their debut album, Linear (1990). Released as the debut single, it was their biggest
Sending_All_My_Love
Group of real 2×2 matrices with unit determinant
In mathematics, the special linear group SL(2, R) or SL2(R) is the group of 2 × 2 real matrices with determinant one: SL ( 2 , R ) = { ( a b c d ) : a
SL2(R)
C_{n}\end{aligned}}} However, since the complex classical Lie groups are linear groups, their representations are tensor representations. Each irreducible
Representations of classical Lie groups
Representations_of_classical_Lie_groups
Mathematical theorem in group theory
generated linear groups. The theorem, proven by Tits, is stated as follows. Theorem— Let G {\displaystyle G} be a finitely generated linear group over a
Tits_alternative
Type of mathematical space
the special linear group over F. Other flag varieties arise by considering partial flags, or by restriction from the special linear group to subgroups
Generalized_flag_variety
Linear function satisfying a support condition
In algebraic geometry, given a linear algebraic group G over a field k, a distribution on it is a linear functional k [ G ] → k {\displaystyle k[G]\to
Distribution on a linear algebraic group
Distribution_on_a_linear_algebraic_group
Method to solve optimization problems
Linear programming (LP), also called linear optimization, is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical
Linear_programming
Lie group whose manifold is complex and whose group operation is holomorphic
group. A complex semisimple Lie group is a linear algebraic group. The Lie algebra of a complex Lie group is a complex Lie algebra. A finite-dimensional
Complex_Lie_group
1990 studio album by Linear
Linear is the name of the debut studio album by the pop/freestyle group Linear. It was released on March 21, 1990, by Atlantic Records. The album's first
Linear_(album)
Non-abelian group of order eight
quaternion group Q8 as a subgroup of the general linear group GL ( 2 , C ) {\displaystyle \operatorname {GL} (2,\mathbb {C} )} . The quaternion group is a
Quaternion_group
Periodic set of points
basis of R n {\displaystyle \mathbb {R} ^{n}} , the subgroup of all linear combinations with integer coefficients of the basis vectors forms a lattice
Lattice_(group)
Concept in mathematics
model for the study of other Lie algebras. The Lie group that it generates is the special linear group. The Lie algebra s l 2 C {\displaystyle {\mathfrak
Special_linear_Lie_algebra
Mathematical concept
L-functions of a connected reductive group are equal to products of automorphic L-functions of general linear groups. A proof of Langlands functoriality
Automorphic_L-function
Square matrix with ones on the main diagonal and zeros elsewhere
In linear algebra, the identity matrix of size n {\displaystyle n} is the n × n {\displaystyle n\times n} square matrix with ones on the main diagonal
Identity_matrix
Group that is a topological space with continuous group operations
number n. The classical groups are important examples of non-abelian topological groups. For instance, the general linear group GL ( n , R ) {\displaystyle
Topological_group
Group in which the order of every element is a power of p
elementary abelian group and its automorphism group is a general linear group, so very well understood. The map from the automorphism group of G into this
P-group
Type of subgroup of an algebraic group
the general linear group GLn (n x n invertible matrices), the subgroup of invertible upper triangular matrices is a Borel subgroup. For groups realized over
Borel_subgroup
Concept in mathematics
result: The mapping class group is residually finite. The proof proceeds first by using residual finiteness of the linear group Sp 2 g ( Z ) {\displaystyle
Mapping class group of a surface
Mapping_class_group_of_a_surface
Syllabic script used for writing Mycenaean Greek
contains Linear B Unicode characters. Without proper rendering support, you may see question marks, boxes, or other symbols instead of Linear B. Linear B is
Linear_B
Subject area in mathematics
space. This gluing data is expressed using the general linear group, but elements of that group coming from elementary matrices (matrices corresponding
Algebraic_K-theory
is an outline of topics related to linear algebra, the branch of mathematics concerning linear equations and linear maps and their representations in vector
Outline_of_linear_algebra
Lie group of Lorentz transformations
homogeneous Lorentz group while the Poincaré group is sometimes called the inhomogeneous Lorentz group. Lorentz transformations are examples of linear transformations;
Lorentz_group
Group representation
Lie group is a linear action of a Lie group on a vector space. Equivalently, a representation is a smooth homomorphism of the group into the group of invertible
Representation_of_a_Lie_group
by pseudoreflections. In the case of subgroups of the complex general linear group the theorem was first proved by G. C. Shephard and J. A. Todd (1954)
Chevalley–Shephard–Todd theorem
Chevalley–Shephard–Todd_theorem
Principal bundle associated to a vector bundle
ordered bases, or frames, for E x {\displaystyle E_{x}} . The general linear group acts naturally on F ( E ) {\displaystyle F(E)} via a change of basis
Frame_bundle
Mathematical group based upon a finite number of elements
classical groups, and other related groups. One such family of groups is the family of general linear groups over finite fields. Finite groups often occur
Finite_group
Upper-half plane model of hyperbolic non-Euclidean geometry
a linear fractional transformation of complex numbers, and the hyperbolic motions are represented by elements of the projective special linear group
Poincaré_half-plane_model
In mathematics, invariant of square matrices
or |A|. Its value characterizes some properties of the matrix and the linear map represented, on a given basis, by the matrix. In particular, the determinant
Determinant
Group without normal subgroups other than the trivial group and itself
second smallest nonabelian simple group is the projective special linear group PSL(2,7) of order 168, and every simple group of order 168 is isomorphic to
Simple_group
Group whose operation is a composition of braids
specializing these variables, the braid group B n {\displaystyle B_{n}} may be realized as a subgroup of the general linear group over the complex numbers. There
Braid_group
\operatorname {\Gamma L} (V),} by analogy with and extending the general linear group. The special case where the field is the complex numbers C {\displaystyle
Semilinear_map
Algebraic structure used in analysis
classification of Lie groups in terms of Lie algebras, which are simpler objects of linear algebra. In more detail: for any Lie group, the multiplication
Lie_algebra
Subgroup invariant under conjugation
normal. As an example of a normal subgroup within a matrix group, consider the general linear group G L n ( R ) {\displaystyle \mathrm {GL} _{n}(\mathbf {R}
Normal_subgroup
Group of rotations in 3 dimensions
equivalently the product of linear transformations). It is a subgroup of the general linear group consisting of all invertible linear transformations of the
3D_rotation_group
Elements taken to zero by a homomorphism
general linear group of n × n {\displaystyle n\times n} matrices of R {\displaystyle \mathbb {R} } , is a homomorphism onto the multiplication group R × {\displaystyle
Kernel_(algebra)
Set of quantum operations
generated by the quantum circuits with Pauli-X and Pauli-Z gates. General linear group GL ( n , F 2 ) {\displaystyle (n,\mathbb {F} _{2})} . It has ∏ j = 0
Clifford_group
Natural number
algebra A 6 {\displaystyle A_{6}} through the special linear group and its corresponding special linear Lie algebra. In the third dimension, there are a total
63_(number)
General linear group Group of Lie type Group scheme HN group Janko group Lie group Simple Lie group Linear algebraic group List of finite simple groups Mathieu
List_of_group_theory_topics
function. GF – Galois field. GF – generating function. GL – general linear group. G.M. – geometric mean. glb – greatest lower bound. (Also written as
List of mathematical abbreviations
List_of_mathematical_abbreviations
Manifold of all orthonormal k-frames in n-dimensional Euclidean space
the compact form, replacing the orthogonal group (or unitary or symplectic group) with the general linear group. Let F {\displaystyle \mathbb {F} } stand
Stiefel_manifold
Mathematical concept
unit complex numbers and the group R+ of positive real numbers under multiplication. If n is odd, then the general linear group GL(n, R) is the internal direct
Direct_product_of_groups
Smallest normal subgroup by which the quotient is commutative
G^{(1)}=G} , it is called a perfect group. This includes non-abelian simple groups and the special linear groups SL n ( k ) {\displaystyle \operatorname
Commutator_subgroup
Sporadic simple group
special group 21+6 by the linear group L3(2), which is the same involution centralizer as the Mathieu group M24. A second such group is the linear group L5(2)
Held_group
Automorphism group of the Klein quartic
In mathematics, the projective special linear group PSL(2, 7), isomorphic to GL(3, 2), is a finite simple group that has important applications in algebra
PSL(2,7)
Isomorphism of differentiable manifolds
the general linear group is also a deformation retract of the full diffeomorphism group. For a finite set of points, the diffeomorphism group is simply
Diffeomorphism
Aspect of group theory in mathematics
as the Tits alternative. The result states that a finitely generated linear group is either virtually solvable or contains a free subgroup of rank two
Ping-pong_lemma
LINEAR GROUP
LINEAR GROUP
Male
Yiddish
 Variant spelling of Yiddish Lieber, LIBER means "beloved." Compare with another form of Liber.
Male
Greek
(ΑἰνÎας) Variant spelling of Greek AineÃas, AINEAS means "praiseworthy."
Surname or Lastname
English (Cornish)
English (Cornish) : habitational name from a place named with Cornish lan ‘church’. In England this surname is now found chiefly in the southern counties of Wiltshire and Hampshire, and Berkshire; it has no doubt moved there from Cornwall.
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).
Surname or Lastname
English
English : occupational name for a whitewasher, Middle English limer, lymer, an agent derivative of Old English līm ‘lime’.
Surname or Lastname
English
English : habitational name from Lingart, Lancashire, or Lingards Wood in Marsden, West Yorkshire, both named from Old English līn ‘flax’ + garðr ‘enclosure’.
Female
English
Variant spelling of English Linsey, LINSAY means "Lincoln's wetlands."
Girl/Female
Irish
Eimear possessed the “Six Gifts of Womanhood†– “beauty, a gentle voice, sweet words, wisdom, needlework and chastity!†She was bethrothed to the warrior Cuchulainn (read the legend) when they were children and they loved each other very deeply. But Cuchulainn had “a wandering eye†and Eimear endured this, realizing “everything new is fair,†but when he made love to Fand, wife of the sea god Manannan, Eimear confronted the lovers. After seeing the strength of Fand’s love she offered to withdraw. Touched by this display of unselfishness, Fand left Cuchulainn and returned to the sea. When Cuchulainn died Eimear spoke movingly and lovingly at his graveside.
Surname or Lastname
English (Devon; of Cornish origin)
English (Devon; of Cornish origin) : topographic name for someone who lived by a menhir, i.e. a tall standing stone erected in prehistoric times (Cornish men ‘stone’ + hir ‘long’).
Female
Scottish
Variant spelling of Scottish Lilias, LILEAS means "lily."
Surname or Lastname
English
English : metronymic from Line.
Boy/Male
Hindu
Lingam
Male
Scandinavian
Scandinavian form of Old Norse Einarr, EINAR means "lone warrior."
Surname or Lastname
Swedish
Swedish : ornamental name from lind ‘lime tree’ + either the German suffix -er denoting an inhabitant, or the surname suffix -ér, derived from the Latin adjectival ending -er(i)us.English (mainly southeastern) : variant of Lind 2.German : habitational name from any of numerous places called Linden or Lindern, named with German Linden ‘lime trees’.
Boy/Male
Irish
Meaning “â€fair-haired,â€â€ the name has been popular since the sixth century when St. Finbar came to an area of Cork that was being tormented by a serpent. The people begged him to do something to help them. One night he went to where the serpent was sleeping and sprinkled it with holy water. The angry serpent tore and devoured the land until she slithered into the sea at Cork Harbor. The track she left behind filled with water and became the River Lee and that’s why St. Finbar is the patron saint of Cork. It is said that the sun didn’t set for two weeks after Finbar’s death.
Boy/Male
Hindu
The Sun
Female
English
English name probably derived from Germanic lindi, LINDA means "serpent."Â In some cases, it may have been derived from the Spanish word for "pretty."
Boy/Male
Sikh
Love unending
Surname or Lastname
English
English : variant of Lanier 1.Dutch : variant of Leonard.Jewish (western Ashkenazic) : name taken by someone who was good at chanting the Pentateuch at public worship in the synagogue or who regularly did so, from West Yiddish layner ‘reader’ (a derivative of West Yiddish laynen ‘to read’, which comes ultimately from Latin legere ‘to read’).Jewish (Ashkenazic) : occupational name for a flax grower or merchant, from German Lein ‘flax’ + agent suffix -er.
Male
English
Irish Anglicized form of Gaelic Fionnbarr, FINBAR means "fair-headed."
LINEAR GROUP
LINEAR GROUP
Boy/Male
Finnish, German, Greek, Portuguese, Swedish
Pious; Devout; Worships Well; Good Worship
Boy/Male
Muslim
Sky
Girl/Female
Tamil
Perceptive or consciousness or life or excellent intelligence, Power of intellect or alert
Girl/Female
British, English, Greek, Irish
Smart; Beautiful Young Child
Boy/Male
Hindu
Girl/Female
Muslim
Name of the first surah in the Quran
Girl/Female
Hindu, Indian
Moonlight
Boy/Male
Hindu, Indian, Tamil
Lord Shiva
Male
Babylonian
, my father is sick.
Girl/Female
Hebrew, Hindu, Indian, Marathi
To Take
LINEAR GROUP
LINEAR GROUP
LINEAR GROUP
LINEAR GROUP
LINEAR GROUP
n.
A dealer in linen; a linen draper.
a.
Linear.
a.
Composed of lines; delineated; as, lineal designs.
a.
Formed by right lines; rectilineal; as, a right-lined angle.
n.
A vessel belonging to a regular line of packets; also, a line-of-battle ship; a ship of the line.
v. t.
To convert into vinegar; to make like vinegar; to render sour or sharp.
n.
A lunar distance.
n.
Alt. of Lingam
n.
Made of linen; as, linen cloth; a linen stocking.
a.
Of, pertaining to, or included by, two lines; as, bilinear coordinates.
n.
One who adjusts things to a line or lines or brings them into line.
a.
Descending in a direct line from an ancestor; hereditary; derived from ancestors; -- opposed to collateral; as, a lineal descent or a lineal descendant.
v. t.
To mark with a line or lines; to cover with lines; as, to line a copy book.
n.
One who lines, as, a liner of shoes.
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.
Of a linear shape.
a.
Like a line; narrow; of the same breadth throughout, except at the extremities; as, a linear leaf.
a.
Of or pertaining to a line; consisting of lines; in a straight direction; lineal.
adv.
In a linear manner; with lines.
prep. & adv.
Near.