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 itself...

is a bijection that maps lines to lines, and thus a collineation. In general, some collineations are not homographies, but the fundamental theorem of...

the plane, the collineation group is doubly transitive meaning that any ordered pair of points can be mapped by at least one collineation to any other ordered...

A matter collineation (sometimes matter symmetry and abbreviated to MC) is a vector field that satisfies the condition, L X T a b = 0 {\displaystyle {\mathcal...

the collineations of PG(2, K) are compositions of homographies and automorphic collineations. Automorphic collineations are planar collineations. A projective...

projective space. A related group is the collineation group, which is defined axiomatically. A collineation is an invertible (or more generally one-to-one)...

A curvature collineation (often abbreviated to CC) is vector field which preserves the Riemann tensor in the sense that, L X R a b c d = 0 {\displaystyle...

is called a perspective collineation (central collineation in more modern terminology). Let φ be a perspective collineation of S2. Each point of the...

sets and so, are collineations. In projective geometry these linear mappings are called homographies and are just one type of collineation. In any triangle...

least three elements, the first condition can be simplified to: f is a collineation, that is, it maps lines to lines. By the definition of an affine space...

An affine vector field (sometimes affine collineation or affine) is a projective vector field preserving geodesics and preserving the affine parameter...

curvature collineations forms a Lie algebra under the Lie bracket operation (if the smoothness condition is dropped, the set of all curvature collineations need...

collineations are easier to define than homographies, and homographies are defined as specific collineations, thus called "projective collineations"...

Die Elemente der Mechanik des Himmels Barycentric coordinate system Collineation Homogeneous coordinates Möbius counter Möbius plane Wells, John C. (2008)...

there exists a central collineation, which maps the one onto the other triangle. But only in special cases this collineation is an affine scaling. For...

Michael Atiyah) 1966: "A representation of the Mathieu group M24 as a collineation group", Ann. Mat. Pura Appl. 71(4), 199-238 Atiyah, M. (1996). "John...

the CRC Reciprocal square root Reciprocity (projective geometry), a collineation from a projective space onto its dual space, taking points to hyperplanes...

alignment, ambilineal, ambilineality, bilinear, collinear, collinearity, collineation, curvilinear, curvilinearity, delineate, delineation, delineavit, line...

motions, whereas in projective geometry an analogous role is played by collineations, geometric transformations that take straight lines into straight lines...

delimit, limes, limit, limitation linea line- line align, collinear, collineation, linea, lineage, linear, linearity, multicollinearity lingua lingu- tongue...

plane corresponding to the Desarguesian plane of order nine since the collineation group of that projective plane acts transitively on the lines of the...

projective semilinear group PΓL(n, F) (which contains PGL(n, F)) is the collineation group of projective space, for n > 2, and thus semilinear maps are of...

Generalised circle Locus Plane (geometry) Polyline Technically, the collineation group acts transitively on the set of lines. On occasion we may consider...

Affine vector field Curvature collineation Homothetic vector field Killing form Killing horizon Killing spinor Matter collineation Spacetime symmetries Jost...

on the same line) to collinear points is called a collineation of the plane. The full collineation group is of order 168 and is isomorphic to the group...

{\displaystyle \mathbb {H} ^{2}} (generated by orientation-preserving collineations). Further, the orthogonal trajectories of these ellipses comprise the...

elements. Another example is provided by the subgroup of order 21 of the collineation group of the Fano plane generated by a 3-fold symmetry σ fixing a point...

the central Steiner conics in the hyperbolic plane produced by direct collineations; and each single-loop is the locus of points P {\displaystyle P} such...

2-transvections. Classifying the intrinsic conics in the hyperbolic plane, using collineation invariants, he offered metric characterizations and highlighted a natural...

be thought of as a collineation between a pair of specially related projective spaces and called a reciprocity. If this collineation is a projectivity...