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Projectivisation
In mathematics, projectivization is a procedure which associates with a non-zero vector space ''V'' a projective space (V), whose elements are one-dimensional Linear subspace, subspaces of ''V''. More generally, any subset ''S'' of ''V'' closed under scalar multiplication defines a subset of (V) formed by the lines contained in ''S'' and is called the projectivization of ''S''. Properties * Projectivization is a special case of the Quotient space (topology), factorization by a Group action (mathematics), group action: the projective space (V) is the quotient of the open set ''V''\ of nonzero vectors by the action of the multiplicative group of the base field by scalar transformations. The dimension (mathematics), dimension of (V) in the sense of algebraic geometry is one less than the dimension of the vector space ''V''. * Projectivization is functorial with respect to injective linear maps: if :: f: V\to W : is a linear map with trivial kernel (linear algebra), kernel then ' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
