Correlation (projective geometry)

This article is about correlation in projective geometry. For other uses, see correlation (disambiguation).

A correlation is a duality (collineation from a projective space onto its dual space, taking points to hyperplanes (and vice versa) and preserving incidence) from a projective space to itself. In the case of projective planes correlations can only exist if the plane is self-dual.

If a correlation σ is involutory (that is, two applications of the correlation equals the identity: σ²(P)=P for all points P) then it is called a polarity.

This geometry-related article is a stub. You can help Wikipedia by expanding it.v · Categories: Projective geometry Geometry stubs Wikimedia Foundation. 2010. Игры ⚽ Поможем написать курсовую Hinterwald Cattle Till Fjälls Look at other dictionaries: Duality (projective geometry) — A striking feature of projective planes is the symmetry of the roles played by points and lines in the definitions and theorems, and (plane) duality is the formalization of this metamathematical concept. There are two approaches to the subject of …   Wikipedia Correlation (disambiguation) — Correlation is a measure of relationship between two mathematical variables or measured data values, which includes the Pearson correlation coefficient as a special case. Correlation may also refer to: Electronic correlation, a description of the …   Wikipedia Reciprocity (projective geometry) — A reciprocity is a collineation from a projective space onto its dual space, taking points to hyperplanes (and vice versa) and preserving incidence.If it can be represented as a homography, it is called a correlation …   Wikipedia Dualité (Géométrie Projective) — La dualité projective, crée par Jean Victor Poncelet (1788 1867), père fondateur de la géométrie projective, bien que beaucoup moins enseignée que la dualité en algèbre linéaire, est probablement la plus belle notion de dualité que l on rencontre …   Wikipédia en Français Dualité (géométrie projective) — Pour les articles homonymes, voir Dualité (mathématiques) et Dualité. La dualité projective, crée par Jean Victor Poncelet (1788 1867), père fondateur de la géométrie projective, bien que beaucoup moins enseignée que la dualité en algèbre… …   Wikipédia en Français List of mathematics articles (C) — NOTOC C C closed subgroup C minimal theory C normal subgroup C number C semiring C space C symmetry C* algebra C0 semigroup CA group Cabal (set theory) Cabibbo Kobayashi Maskawa matrix Cabinet projection Cable knot Cabri Geometry Cabtaxi number… …   Wikipedia List of mathematics articles (P) — NOTOC P P = NP problem P adic analysis P adic number P adic order P compact group P group P² irreducible P Laplacian P matrix P rep P value P vector P y method Pacific Journal of Mathematics Package merge algorithm Packed storage matrix Packing… …   Wikipedia Collineation — 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, such that the images of collinear points are themselves collinear. All projective linear …   Wikipedia Forme hermitienne — Cet article concerne le cas général abstrait. Pour un cas plus élémentaire, voir Forme sesquilinéaire complexe. En mathématiques, une forme hermitienne est une fonction de deux variable sur un espace vectoriel sur un corps relativement à une… …   Wikipédia en Français Scale invariance — In physics and mathematics, scale invariance is a feature of objects or laws that do not change if length scales (or energy scales) are multiplied by a common factor. The technical term for this transformation is a dilatation (also known as… …   Wikipedia 18+ © Academic, 2000-2024 Contact us: Technical Support, Advertising Dictionaries export, created on PHP, Joomla, Drupal, WordPress, MODx. Mark and share Search through all dictionaries Translate… Search Internet Share the article and excerpts Direct link … Do a right-click on the link above and select “Copy Link”