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Subspace
Subspace may refer to: In mathematics * A space inheriting all characteristics of a parent space * A subset of a topological space endowed with the subspace topology * Linear subspace, in linear algebra, a subset of a vector space that is closed under addition and scalar multiplication * Flat (geometry), a Euclidean subspace * Affine subspace, a geometric structure that generalizes the affine properties of a flat * Projective subspace, a geometric structure that generalizes a linear subspace of a vector space * Multilinear subspace Multilinear subspace learning is an approach to dimensionality reduction.M. A. O. Vasilescu, D. Terzopoulos (2003"Multilinear Subspace Analysis of Image Ensembles" "Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVP ... in multilinear algebra, a subset of a tensor space that is closed under addition and scalar multiplication In science fiction * a concept similar to that of hyperspace * Subspace (''Star Trek''), a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linear Subspace
In mathematics, and more specifically in linear algebra, a linear subspace, also known as a vector subspaceThe term ''linear subspace'' is sometimes used for referring to flats and affine subspaces. In the case of vector spaces over the reals, linear subspaces, flats, and affine subspaces are also called ''linear manifolds'' for emphasizing that there are also manifolds. is a vector space that is a subset of some larger vector space. A linear subspace is usually simply called a ''subspace'' when the context serves to distinguish it from other types of subspaces. Definition If ''V'' is a vector space over a field ''K'' and if ''W'' is a subset of ''V'', then ''W'' is a linear subspace of ''V'' if under the operations of ''V'', ''W'' is a vector space over ''K''. Equivalently, a nonempty subset ''W'' is a subspace of ''V'' if, whenever are elements of ''W'' and are elements of ''K'', it follows that is in ''W''. As a corollary, all vector spaces are equipped with at least two ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
