Definition, Betydelse & Synonymer | Engelska ordet SUBSPACE

Definition av SUBSPACE

1. (matematik) underrum

Exempel på hur man kan använda SUBSPACE i en mening

• Projective cone, the union of all lines that intersect a projective subspace and an arbitrary subset of some other disjoint subspace.
• When defined for a topological vector space, there is a subspace of the dual space, corresponding to continuous linear functionals, called the continuous dual space.
• It allows the extension of bounded linear functionals defined on a vector subspace of some vector space to the whole space, and it also shows that there are "enough" continuous linear functionals defined on every normed vector space to make the study of the dual space "interesting".
• Left (or right) radical of a bilinear form, the subspace of all vectors left (or right) orthogonal to every vector.
• Multilinear subspace in multilinear algebra, a subset of a tensor space that is closed under addition and scalar multiplication.
• A subalgebra of an algebra over a commutative ring or field is a vector subspace which is closed under the multiplication of vectors.
• In mathematics, a Clifford algebra is an algebra generated by a vector space with a quadratic form, and is a unital associative algebra with the additional structure of a distinguished subspace.
• If X is a Tychonoff space then the map from X to its image in βX is a homeomorphism, so X can be thought of as a (dense) subspace of βX; every other compact Hausdorff space that densely contains X is a quotient of βX.
• That is, a nonempty set W is a subspace if and only if every linear combination of finitely many elements of W also belongs to W.
• An example of this situation is the adele ring of a global field; its unit group, called the idele group, is not a topological group in the subspace topology.
• 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.
• Like a plane in space, a hyperplane is a flat hypersurface, a subspace whose dimension is one less than that of the ambient space.
• If f is injective, this topology is canonically identified with the subspace topology of S, viewed as a subset of X.
• In linear algebra, orthogonalization is the process of finding a set of orthogonal vectors that span a particular subspace.
• Suppose by way of contradiction that there is some strict total order < on Z such that the order topology generated by < is equal to the subspace topology on Z (note that we are not assuming that < is the induced order on Z, but rather an arbitrarily given total order on Z that generates the subspace topology).
• Among other contexts, ego reduction has been seen as a goal in Alcoholics Anonymous; as a part of BDSM play, providing a means of entering "subspace"; and as a way of attaining religious humility and freedom from desire in Buddhism.
• This follows from the previous result about completely metrizable subspaces and the fact that every subspace of a separable metric space is separable.
• The complex analog to a Lagrangian subspace is a real subspace, a subspace whose complexification is the whole space:.
• If V is finite-dimensional, then V is completely reducible if and only if every invariant subspace of V has an invariant complement.
• With Bernard Maurey he resolved the "unconditional basic sequence problem" in 1992, showing that not every infinite-dimensional Banach space has an infinite-dimensional subspace that admits an unconditional Schauder basis.

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