# projective

Jump to navigation
Jump to search

## English

[edit]### Etymology

[edit]Formed by the suffixation of *prōiect-* (the perfect passive participial stem of the Classical Latin *prōiciō*, whence the English verb *project*) with the English *-ive*; however, compare the post-Classical Latin *prōiectīvus* (“relating to purging”).

### Pronunciation

[edit]- Rhymes: -ɛktɪv

### Adjective

[edit]**projective** (*comparative* **more projective**,

*superlative*

**most**)

**projective**- projecting outward
- of, relating to, or caused by a projection
- (geometry) Of or related to projective geometry:
- (now usually in set phrases, of a property of a geometric object, figure, etc.) Invariant under projective transformations.
**1912**November, 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:- 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.

- (of a geometric object, figure, etc.) Defined in or inhabiting a projective space.

- (now usually in set phrases, of a property of a geometric object, figure, etc.) Invariant under projective transformations.
- (algebra) In a technical sense, general (but not necessarily so general as to be free); involving such objects:
- (module theory, of a (left) module over a ring ) Such that there is another (left) -module with a free -module. Equivalently, projective in the category of modules (see below).
- (category theory, most generally, of an object in a category) Such that, given an epimorphism and morphism , factors through ; that is, there exists a morphism with .
- (group theory, of a profinite group ) Such that every epimorphism from a profinite group onto has a right inverse which is a homomorphism.
- (homological algebra, of a resolution) Such that every object in the resolution is projective.

#### Derived terms

[edit]### Noun

[edit]**projective** (*plural* **projectives**)

- (psychology) An assessment test that presents subjects with some sort of stimulus to which they react by projecting or imagining details.
**1984**, Lawrence A. Pervin, Personality: Theory and Research, →ISBN, page 322:- The
**projectives**suggested considerable difficulty with women and a conflict between sexual preoccupation and hostility.

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

**2012**, Linda C. Wing, Bernard R. Gifford, Policy Issues in Employment Testing, →ISBN, page 174:- The unimpressive evidence for validity and operational problems related to
**projectives**led Reilly and Chao to a pessimistic conclusion regarding**projectives**.

**2015**, Paul Hackett, Qualitative Research Methods in Consumer Psychology, →ISBN:- 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.

- (mathematics) A projective member of a category.
**1965**, Theory of Categories, →ISBN, page 109:- 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**.

**1999**, Maurice Auslander, Idun Reiten, Sverre O. Smalø, Selected Works of Maurice Auslander - Part 1, →ISBN, page 490:- In particular our assumptions hold if B is an abelian category with enough
**projectives**.

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

- (linguistics) A statement about a conditional or potential state of affairs, as opposed to one about a situation that actually exists or existed.
**1995**, Keith E. Nelson, Zita Reger, Children's Language - Volume 8, →ISBN:- There was no basis for expecting differences in the frequency of
**projectives**or turnabouts as a function of partner.

**2007**, Ronald James Williams, John C. Beckman, Williams' Hebrew Syntax, →ISBN, page 78:- The volitive moods (also called volitives, volitional forms, modals, or
**projectives**) are the imperative, jussive, and cohortative.

**2012**, Jean Curthoys, Victor Dudman, Victor Dudman's Grammar and Semantics, →ISBN, page 74:- 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.

#### Derived terms

[edit]- biprojective
- multiprojective
- nonprojective
- preprojective
- projective algebraic manifold
- projective collineation
- projective cone
- projective correlation
- projective differential geometry
- projective frame
- projective general linear group
- projective general orthogonal group
- projective general unitary group
- projective geometry
- projective Hilbert space
- projective identification
- projective limit
- projective line
- projective linear group
- projectively
- projective module
- projective object
- projective plane
- projective plane dissection
- projective representation
- projective set
- projective space
- projective special linear group
- projective special orthogonal group
- projective special unitary group
- projective symplectic group
- projective test
- projective texture mapping
- projective transformation
- projective unitary group
- projective variety
- projective vector field
- projectivism
- quasiprojective
- semiprojective
- superprojective

### Related terms

[edit]## French

[edit]### Pronunciation

[edit]- IPA
^{(key)}: /pʁɔ.ʒɛk.tiv/ - Homophone: projectives

### Adjective

[edit]**projective**

Categories:

- English terms derived from Latin
- Rhymes:English/ɛktɪv
- Rhymes:English/ɛktɪv/3 syllables
- English lemmas
- English adjectives
- en:Geometry
- English terms with quotations
- en:Algebra
- en:Group theory
- English nouns
- English countable nouns
- en:Psychology
- en:Mathematics
- en:Linguistics
- English terms suffixed with -ive
- French 3-syllable words
- French terms with IPA pronunciation
- French terms with homophones
- French non-lemma forms
- French adjective forms