# 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 [14], 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 [2] has shown that k must, in fact, divide t.
In [13] 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.
[11] 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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