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...

In mathematics, the orthogonal group in dimension n, denoted O(n), is the group of distance-preserving transformations of a Euclidean space of dimension...

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 geometry, a (globally) projective polyhedron is a tessellation of the real projective plane. These are projective analogs of spherical polyhedra – tessellations...

group is a certain subgroup of the Clifford algebra associated to a quadratic space. It maps 2-to-1 to the orthogonal group, just as the spin group maps...

general linear group of a vector space V on the associated projective space P(V). Explicitly, the projective linear group is the quotient group PGL(V) = GL(V) / Z(V)...

cover the special orthogonal groups, which (in even dimension) doubly cover the projective orthogonal group. the metaplectic groups, which double cover...

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

the orthogonal group O(n) has the special orthogonal group SO(n) as subgroup and the projective orthogonal group PO(n) as quotient, and the projective special...

passing to the projective orthogonal group. In dimension 2 these groups completely describe the hyperoctahedral group, which is the dihedral group Dih4 of order...

monoxide (PO), an unstable radical inorganic compound Projective orthogonal group, an action in projective geometry and linear algebra Per os or peroral, meaning...

orthogonal group SOn(R) and quotients, the projective orthogonal group POn(R), and the projective special orthogonal group PSOn(R). In characteristic 2 the determinant...

SO(n − 1) Projective space (projective orthogonal group): Pn−1 ≅ PO(n) / PO(n − 1) Flat (zero curvature): Euclidean space (Euclidean group, point stabilizer...

× n orthogonal matrices, under multiplication, forms the group O(n), known as the orthogonal group. The subgroup SO(n) consisting of orthogonal matrices...

standard round metric, the measure of projective space is exactly half the measure of the sphere. Real projective spaces are smooth manifolds. On Sn, in...

real projective plane, denoted ⁠ R P 2 {\displaystyle \mathbf {RP} ^{2}} ⁠ or ⁠ P 2 {\displaystyle \mathbb {P} _{2}} ⁠, is a two-dimensional projective space...

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 (...

the simple group is not the orthogonal group O, nor the projective special orthogonal group PSO, but rather a subgroup of PSO, which accordingly does...

multiplication, the rotation group is isomorphic to the special orthogonal group SO(3). Improper rotations correspond to orthogonal matrices with determinant...

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

extendable to a finite projective plane of the same order, this equivalence can also be expressed in terms of the existence of these projective planes. As mentioned...

centerless compact group the projective unitary group PU(r + 1). Br has as its associated centerless compact groups the odd special orthogonal groups, SO(2r + 1)...

group P O ( n , 1 ) {\displaystyle \mathrm {PO} (n,1)} (the projective orthogonal group of a quadratic form of signature ( n , 1 ) {\displaystyle (n...

PSL – projective special linear group. PNT – prime number theorem. PRP – probable prime. PSO – projective orthogonal group. PSU – projective special...

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

algebraic groups belongs both to algebraic geometry and group theory. Many groups of geometric transformations are algebraic groups, including orthogonal groups...

In projective geometry, the harmonic conjugate point of a point on the real projective line with respect to two other points is defined by the following...

complex projective space is the projective space with respect to the field of complex numbers. By analogy, whereas the points of a real projective space...

shear mappings. Presuming knowledge of projectivity and the projective group of projective geometry, the affine group can be easily specified. For example...

to mean a projective homogeneous variety, that is, a smooth projective variety X over a field F with a transitive action of a reductive group G (and smooth...