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...

collineation group of projective space, for n > 2 {\displaystyle n>2} , and thus semilinear maps are of interest in projective geometry. The Full Linear Monoid...

In projective geometry and linear algebra, the projective orthogonal group PO is the induced action of the orthogonal group of a quadratic space V = (V...

mathematics, a projective representation of a group G on a vector space V over a field F is a group homomorphism from G to the projective linear group P G L (...

SL(2, R) SL(2, C) Modular group (PSL(2, Z)) Projective linear group Conformal map Representations of classical Lie groups Hall 2015 Section 2.5 Hall...

one-dimensional linear subspaces of a two-dimensional vector space over the reals. The automorphisms of a real projective line are called projective transformations...

a field, a linear fractional transformation is the restriction to the field of a projective transformation or homography of the projective line. When...

Jordan's theorem that the projective special linear group PSL(2, q) is simple for q ≠ 2, 3. This theorem generalizes to projective groups of higher dimensions...

the field extension. The automorphism group of the projective n-space over a field k is the projective linear group PGL n ⁡ ( k ) . {\displaystyle \operatorname...

k-tuples of points are not in general position. While the projective linear group of the projective line is 3-transitive (any three distinct points can be...

that the projective groups associated to these groups are also linear, though less obviously. For example, the group PSL2(R) is not a group of 2 × 2 matrices...

Projective space Projective transformation Projective geometry Projective linear group Quadric and conic section Glossary of linear algebra Glossary of...

the complex projective plane, and finite, such as the Fano plane. A projective plane is a 2-dimensional projective space. Not all projective planes can...

holomorphic isometry group of complex projective space, just as the projective orthogonal group is the isometry group of real projective space. In terms of...

In projective geometry, a homography is an isomorphism of projective spaces, induced by an isomorphism of the vector spaces from which the projective spaces...

concept of a projective space originated from the visual effect of perspective, where parallel lines seem to meet at infinity. A projective space may thus...

In mathematics, projective geometry is the study of geometric properties that are invariant with respect to projective transformations. This means that...

mathematics, projective group may refer to: Projective linear group or one of the related linear groups Projective orthogonal group Projective unitary group Projective...

11 in humans for the group P G L 2 {\displaystyle \mathrm {PGL} _{2}} in mathematics, see projective linear group and modular group This disambiguation...

are the projective transformations of the complex projective line. They form a group called the Möbius group, which is the projective linear group PGL(2...

Galois cohomology classes in H1(G(Ks/K),PGLn), where PGLn is the projective linear group, and n is one more than the dimension of the variety V. As usual...

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

In linear algebra, particularly projective geometry, a semilinear map between vector spaces V and W over a field K is a function that is a linear map "up...

the action of the general linear group on projective space. Particularly notable is PGL(2, K), the symmetries of the projective line, which is sharply 3-transitive...

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

by fractional linear transformations. The group action factors through the quotient PSL(2, R) (the 2 × 2 projective special linear group over R). More...

p≥5 the projective special linear groups PSL2(9) the projective special linear groups PSL2(2n) for n≥2 the projective special linear groups PSL3(2n)...

interpretation of the Brauer group of a field K is that it classifies the projective varieties over K that become isomorphic to projective space over an algebraic...

In projective geometry, a collineation is a one-to-one and onto map (a bijection) from one projective space to another, or from a projective space to...

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