Information om | Engelska ordet SUBSPACES

Exempel på hur man kan använda SUBSPACES i en mening

• A topological space is a set endowed with a structure, called a topology, which allows defining continuous deformation of subspaces, and, more generally, all kinds of continuity.
• More generally, an affine transformation is an automorphism of an affine space (Euclidean spaces are specific affine spaces), that is, a function which maps an affine space onto itself while preserving both the dimension of any affine subspaces (meaning that it sends points to points, lines to lines, planes to planes, and so on) and the ratios of the lengths of parallel line segments.
• From the definition of vector spaces, it follows that subspaces are nonempty, and are closed under sums and under scalar multiples.
• In algebra, another area of mathematics, addition can also be performed on abstract objects such as vectors, matrices, subspaces and subgroups.
• In terms of 3-dimensional geometric vectors, these affine subspaces are all the "lines" or "planes" parallel to the subspace, which is a line or plane going through the origin.
• He introduced the Grassmannian, the space which parameterizes all k-dimensional linear subspaces of an n-dimensional vector space V.
• In higher dimensional spaces there are considered hyperplanes (that always meet), and other linear subspaces, which exhibit the principle of duality.
• This follows from the previous result about completely metrizable subspaces and the fact that every subspace of a separable metric space is separable.
• The "Beurling factorization" helped mathematical scientists to understand the Wold decomposition, and inspired further work on the invariant subspaces of linear operators and operator algebras, e.
• is the Klein four-group, with each factor being whether an element preserves or reverses the respective orientations on the p and q dimensional subspaces on which the form is definite; note that reversing orientation on only one of these subspaces reverses orientation on the whole space.
• In mathematics, a topological space is said to be σ-compact if it is the union of countably many compact subspaces.
• The method consists of splitting a space into subspaces, for which the homology or cohomology groups may be easier to compute.
• A flag in a finite dimensional vector space V over a field F is an increasing sequence of subspaces, where "increasing" means each is a proper subspace of the next (see filtration):.
• In an infinite-dimensional space V, as used in functional analysis, the flag idea generalises to a subspace nest, namely a collection of subspaces of V that is a total order for inclusion and which further is closed under arbitrary intersections and closed linear spans.
• In a finite geometry of higher dimension, X could be the set of points and Y could be the set of subspaces of dimension one less than the dimension of the entire space (hyperplanes); or, more generally, X could be the set of all subspaces of one dimension d and Y the set of all subspaces of another dimension e, with incidence defined as containment.
• Decoherence-free subspaces, subspace of a system's Hilbert space where the system is decoupled from the environment.
• Since the orthogonal projections corresponding to the subspaces in a nest commute, nests are commutative subspace lattices.
• In mathematics, codimension is a basic geometric idea that applies to subspaces in vector spaces, to submanifolds in manifolds, and suitable subsets of algebraic varieties.
• When V is a finite-dimensional vector space over an algebraically closed field, linear transformations acting on V are characterized (up to similarity) by the Jordan canonical form, which decomposes V into invariant subspaces of T.
• It has three subspaces: wetlands and lowlands, which are prone to flooding as they are located along the Ottawa River; the indentations and embankments of the Rigaud and Raquette rivers; and, the flat terrace, which makes up most of the territory.

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