projective

comparative more projective · superlative most projective

1. projecting outward

   Synonyms: outstanding, projecting, prominent, bulging, exserted, extuberant, jutting, obtrusive

2. of, relating to, or caused by a projection

   Synonyms: projectory

3. Of or related to projective geometry:
   1. usuallynow usually in set phrases; figure; now usually in set phrases; figuregeometryInvariant under projective transformations.

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      Hence the non-Euclidean angle is measured by one-half the logarithm of the cross-ratio of four rays. Although the Euclidean point of view has been adopted for simplicity, the final result, depending as it does only on the cross-ratio, is projective; it is therefore independent of the particular assumptions that the rays α and β are perpendicular and that the initial line bisects the angle between them.

      1912 November 28, Edwin B. Wilson, Gillbert B. Lewis, “The Space-Time Manifold of Relativity. The Non-Euclidean Geometry of Mechanics and Electromagnetics”, in Proceedings of the American Academy of Arts and Sciences, volume 45, number 11, page 503

   2. usuallyfiguregeometryDefined in or inhabiting a projective space.
4. In a technical sense, general (but not necessarily so general as to be free); involving such objects:
   1. module theoryalgebraSuch that there is another (left) R-module N with M⊕N a free R-module. Equivalently, projective in the category of modules (see below).
   2. most generallyalgebraSuch that, given an epimorphism e:E→X and morphism f:P→X, f factors through e; that is, there exists a morphism ̃f:P→E with e∘̃f=f.
   3. algebraSuch that every epimorphism from a profinite group onto G has a right inverse which is a homomorphism.
   4. homological algebraalgebraSuch that every object in the resolution is projective.

plural projectives

1. human sciencesAn assessment test that presents subjects with some sort of stimulus to which they react by projecting or imagining details.

   The projectives suggested considerable difficulty with women and a conflict between sexual preoccupation and hostility.

   1984, Lawrence A. Pervin, Personality: Theory and Research, →ISBN, page 322

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   For example, using projectives as a psychometric technique allows one to compare a person's score with those from a normative group, or with those from some relevant clinic group, or with some other clinically important criterion (e.g., response to treatment).

   2009, Paul J. Frick, Christopher T. Barry, Randy W. Kamphaus, Clinical Assessment of Child and Adolescent Personality and Behavior, →ISBN

   The unimpressive evidence for validity and operational problems related to projectives led Reilly and Chao to a pessimistic conclusion regarding projectives.

   2012, Linda C. Wing, Bernard R. Gifford, Policy Issues in Employment Testing, →ISBN, page 174

   With its origins based in the field of psychology, projectives (also referred to as projective exercises or projective techniques) when used in qualitative research are fun "assignments" most often implemented during focus groups. Their goal is to elicit deeper, more visceral feelings from respondents -- about brands, products, concepts, advertising, and so on -- viewpoints that may go unmentioned when using more direct lines of inquiry.

   2015, Paul Hackett, Qualitative Research Methods in Consumer Psychology, →ISBN

2. mathematicsA projective member of a category.

   In particular our assumptions hold if B is an abelian category with enough projectives.

   1999, Maurice Auslander, Idun Reiten, Sverre O. Smalø, Selected Works of Maurice Auslander - Part 1, →ISBN, page 490

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   By 2.2 we see that this is a full, contravariant imbedding, and by 2.3 the image of A in (A, G) is a generating set of small projectives.

   1965, Theory of Categories, →ISBN, page 109

   The idea behind “cheating with projectives” in a pre-Abelian category with a separating class of projectives is this: Make the arrows do the work that elements do in concrete categories.

   2012, M. Scott Osborne, Basic Homological Algebra, →ISBN, page 187

3. human sciencesA statement about a conditional or potential state of affairs, as opposed to one about a situation that actually exists or existed.

   There was no basis for expecting differences in the frequency of projectives or turnabouts as a function of partner.

   1995, Keith E. Nelson, Zita Reger, Children's Language - Volume 8, →ISBN

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   The volitive moods (also called volitives, volitional forms, modals, or projectives) are the imperative, jussive, and cohortative.

   2007, Ronald James Williams, John C. Beckman, Williams' Hebrew Syntax, →ISBN, page 78

   This implies they contain more information than projectives. For if language is a code, then every element of that code – here, every word, every form of a word – would register a distinct semantic ingredient.

   2012, Jean Curthoys, Victor Dudman, Victor Dudman's Grammar and Semantics, →ISBN, page 74