Phrase Hound found 22 phrases and 12 compound words that contain projective. The most common are listed below. Open projective in the live search for definitions, filters, and the full list.
Phrases 22
- projective geometryThe branch of mathematics that investigates those properties of figures that are invariant under homographies, special kinds of spaces called projective spaces, and the geometric structures that inhabit them.
- projective varietyA Zariski closed subvariety of a projective space; the zero-locus of a set of homogeneous polynomials that generates a prime ideal.
- projective lineA line that includes a point at infinity; a line in a projective space; a projective space of dimension 1.
- projective spaceA kind of geometrical space in which only relation(s) of incidence between points and lines matter; in such a space distances or angles do not matter and parallelism (as in an affine space) does not matter either.
- projective planeA plane in which any pair of distinct points determine a line and any pair of distinct lines intersect at a point.
- complex projective lineA complex line (especially, the set of complex numbers regarded as such) endowed with a point at infinity (thus becoming a projective line); (more formally) the set of equivalence classes of ordered pairs (α, β) of complex numbers, not …
- projective frameThe projection onto an n − 1 dimensional hyperplane (which is extended so as to be projective) of a set of n + 1 affinely independent n-dimensional points (called an affine frame).
- projective limitSynonym of limit (“the cone of a diagram through which any other cone of that same diagram can factor uniquely”)
- projective moduleA module which is a direct summand of a free module.
- projective modulesplural of projective module: A module which is a direct summand of a free module.
- projective spacesplural of projective space: A kind of geometrical space in which only relation(s) of incidence between points and lines matter; in such a space distances or angles do not matter and parallelism (as in an affine space) does not matter …
- projective varietiesplural of projective variety: A Zariski closed subvariety of a projective space; the zero-locus of a set of homogeneous polynomials that generates a prime ideal.
- quasi-projectiveLocally closed with respect to the Zariski topology on projective n-space; isomorphic to such a set.
- projective Hilbert spaceThe quotient of a Hilbert space by an equivalence relation which considers a pair of vectors equivalent iff they differ only by a factor which is a complex number.
- real projective planeA three-dimensional vector space over the field of real numbers in which one-dimensional linear subspaces are considered as “points” and two-dimensional linear subspaces are considered as “lines”. Equivalently, a sphere in which pairs of …
- projective framesplural of projective frame: The projection onto an n − 1 dimensional hyperplane (which is extended so as to be projective) of a set of n + 1 affinely independent n-dimensional points (called an affine frame).
- projective limitsplural of projective limit: Synonym of limit (“the cone of a diagram through which any other cone of that same diagram can factor uniquely”)
- projective linesplural of projective line: A line that includes a point at infinity; a line in a projective space; a projective space of dimension 1.
- projective planesplural of projective plane: A plane in which any pair of distinct points determine a line and any pair of distinct lines intersect at a point.
- projective Hilbert spacesplural of projective Hilbert space: The quotient of a Hilbert space by an equivalence relation which considers a pair of vectors equivalent iff they differ only by a factor which is a complex number.
- complex projective linesplural of complex projective line: A complex line (especially, the set of complex numbers regarded as such) endowed with a point at infinity (thus becoming a projective line); (more formally) the set of equivalence classes of ordered pairs …
- real projective planesplural of real projective plane: A three-dimensional vector space over the field of real numbers in which one-dimensional linear subspaces are considered as “points” and two-dimensional linear subspaces are considered as “lines” …
Compound words 12
- projectivizationA process (more formally, a mapping) that, given a vector space, specifies an associated projective space; (loosely) the projective space so specified.
- biprojectiveActing as both a projective left and right module, such that the left and right multiplications are compatible.
- preprojectiveExhibiting a generalization of being projective, in which some, but not every surjective homomorphism splits.
- projectivistRelating to projectivism.
- projectivityThe condition of being projective.
- semiprojectivePartially projective
- nonprojectiveNot projective.
- projectivelyIn a projective way.
- projectiviseThe process of transforming a mathematical object into its projective form, often by embedding it into a projective space.
- projectivismA philosophy in which the qualities of an object are 'projected' onto it as though they actually belong to it.