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...

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...

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...

Linear (pronounced: /lɪˈnɪər/; lin-EER) is an American freestyle-pop group from Fort Lauderdale, Florida. The lineup originally consisted of founder, lead...

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

In mathematics, the special linear group SL ⁡ ( n , R ) {\displaystyle \operatorname {SL} (n,R)} of degree n {\displaystyle n} over a commutative ring...

group of rational points of a reductive linear algebraic group with values in a finite field. The phrase group of Lie type does not have a widely accepted...

contains Linear A Unicode characters. Without proper rendering support, you may see question marks, boxes, or other symbols instead of Linear A. Linear A is...

The Lorentz group is a 6-dimensional Lie group of linear isometries of the Minkowski space. The Poincaré group is a 10-dimensional Lie group of affine isometries...

In linear algebra, the trace of a square matrix A, denoted tr(A), is the sum of the elements on its main diagonal, a 11 + a 22 + ⋯ + a n n {\displaystyle...

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 ⁡ (...

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...

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...

mathematical field of representation theory, group representations describe abstract groups in terms of bijective linear transformations of a vector space to...

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...

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 ⋊...

orthogonal groups, general linear groups, projective groups, Euclidean groups, etc. Many matrix groups are also algebraic. Other algebraic groups occur naturally...

unitary group is a subgroup of the general linear group GL(n, C), and it has as a subgroup the special unitary group, consisting of those unitary matrices...

In mathematics, the modular group is the projective special linear group PSL ⁡ ( 2 , Z ) {\displaystyle \operatorname {PSL} (2,\mathbb {Z} )} of 2 × 2...

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...

{\displaystyle \mathbb {C} ^{n}} . It is itself a subgroup of the general linear group, SU ⁡ ( n ) ⊂ U ⁡ ( n ) ⊂ GL ⁡ ( n , C ) . {\displaystyle \operatorname...

specifically in linear algebra, a linear map (also called a linear mapping, linear transformation, vector space homomorphism, or in some contexts linear function)...

In statistics, linear regression is a model that estimates the relationship between a scalar response (dependent variable) and one or more explanatory...

projective transformations, homographies, or linear fractional transformations. They form the projective linear group PGL(2, R). Each element of PGL(2, R) can...

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...

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...

In mathematics, a linear fractional transformation is, roughly speaking, an invertible transformation of the form z ↦ a z + b c z + d . {\displaystyle...

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...

studies abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studies modules over these abstract...

complex group and Abelian linear group, and is the Greek analog of "complex". The metaplectic group is a double cover of the symplectic group over R;...