Definition of Collineations. Meaning of Collineations. Synonyms of Collineations

Here you will find one or more explanations in English for the word Collineations. Also in the bottom left of the page several parts of wikipedia pages related to the word Collineations and, of course, Collineations synonyms and on the right images related to the word Collineations.

Definition of Collineations

Collineation
Collineation Col*lin`e*a"tion, n. [L. collineare to direct in a straight line. See Collimation.] The act of aiming at, or directing in a line with, a fixed object. [R.] --Johnson.

Meaning of Collineations from wikipedia

- central collineation, when the dimension of P is at least two. (See § Central collineations below and Perspectivity § Perspective collineations.) Originally...
- the collineations of PG(2, K) are compositions of homographies and automorphic collineations. Automorphic collineations are planar collineations. A projective...
- and it can be shown that the number of collineations fixing a configuration equals the number of collineations that fix its dual configuration. There...
- } This last requirement ensures that collineations are all semilinear maps. The main examples of collineations are projective linear transformations...
- incidence relation, which is exactly a collineation of a space to itself. Projective linear transforms are collineations (planes in a vector space correspond...
- 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"...
- curvature collineations forms a Lie algebra under the Lie bracket operation (if the smoothness condition is dropped, the set of all curvature collineations need...
- 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...