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 (...

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

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...

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...

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

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...

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...

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

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...

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...

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

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...

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

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...

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 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...

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

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...

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...

each cell (60). The symmetry structure is the abstract group projective special linear group of the 2-dimensional vector space over the finite field...

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

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...

are conjugate. The projective linear group of dimension two over the finite field with five elements, PGL(2, 5), acts on the projective line over the field...

Ihara, Yasutaka (1966). "On discrete subgroups of the two by two projective linear group over p {\displaystyle {\mathfrak {p}}} -adic fields". Journal of...

general ring A, a projective line over A can be defined with homogeneous factors acting on the left and the projective linear group acting on the right...