# collineation

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Related to collineation: Homography, projective geometry

## collineation

[kə‚lin·ē′ā·shən]
(mathematics)
A mapping which transforms points into points, lines into lines, and planes into planes. Also known as collineatory transformation.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
Otherwise, a collineation of the affine plane A is a bijection of set P on yourself , that preserves lines.
If two segments are intersected in a general case, the value of [P.sub.s] is 2; for the special case of collineation, it is 1, otherwise 0 (Figure 11, right).
In this projective framework, the central collineation fields [H.sub.o,p] are defined such that at each p they are particular changes of projective frames [F.sub.p].
In this paper, we present a mathematical model of almost Ricci soliton (ARS) semi-Riemannian manifolds which also admit a connection symmetry, called "conformal collineations" (Definition 1) and a physical model of almost Ricci soliton imperfect fluid (in particular, viscous fluid) spacetimes of general relativity.
The two-dimensional projectivities (collineation and correlation) are included in the Curriculum Course of Synthetic Geometry.
This correspondence is a collineation of the parabolic subspace [[N>.sub.k] to the index m Grassmann space of [[N>.sub.k-m].
The linear relationship from Figure 9 was transferred into the graph in Figure 10 by plotting a line from the pole of collineation to the centroid of points limited by the equation [q.sub.dry] - ([q.sub.i] - [q.sub.sw] ) = [+ or -]4.8 (W * [m.sup.-2]) = [+ or -]1.52 (Btu * [h.sup.-1] * [ft.sup.-2]) in Figure 9.
A one-to-one map f : S [right arrow] S of a betweenness plane onto itself is said to be a collineation if (abc) [??] (f(a)f(b)f(c)), i.e.
More generally, if a finite translation plane [pi] of order [p.sup.t] admits a collineation of order p that fixes an affine subplane [[pi].sub.0] of order [p.sup.k] pointwise, then Foulser  has shown that k must, in fact, divide t.
In  the notions "collineation" and "flag" are defined in betweenness geometry, and also the notion "group of collineations" is introduced by appropriate axioms.
Coxeter, Desargues configurations and their collineation groups, Math.
 classified static plane symmetric space-time according to their Ricci collineations (RCs) and their relation with isometries of the space-time.

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