In linear algebra, a reducing subspace W {\displaystyle W} of a linear map T : V → V {\displaystyle T:V\to V} from a Hilbert space V {\displaystyle V}...

linear subspace or vector subspace is a vector space that is a subset of some larger vector space. A linear subspace is usually simply called a subspace when...

estimate an effective dimension reducing subspace, it is now understood that it estimates only the central subspace, which is generally different. More...

proves the invariant subspace claim. In fact, one can conclude something stronger. The range of EB is actually a reducing subspace of A, i.e. its orthogonal...

decomposition LU decomposition QR decomposition Polar decomposition Reducing subspace Spectral theorem Singular value decomposition Higher-order singular...

k {\displaystyle k} -dimensional subspaces w ⊂ V {\displaystyle w\subset V} whose intersections with the subspaces { V j } j = 1 , … , n {\displaystyle...

methods are the stationary iterative methods, and the more general Krylov subspace methods. Stationary iterative methods solve a linear system with an operator...

number of possible values with each dimension, complete enumeration of all subspaces becomes intractable with increasing dimensionality. This problem is known...

SubSpace is a 2D space shooter video game created in 1995 and released in 1997 by Virgin Interactive which was a finalist for the Academy of Interactive...

subspaces: its Euclidean subspaces and its linear subspaces. Linear subspaces are Euclidean subspaces and a Euclidean subspace is a linear subspace if...

principal components, and the PCA subspace spanned by the principal directions is identical to the cluster centroid subspace. However, that PCA is a useful...

space V is called semi-simple if every T-invariant subspace has a complementary T-invariant subspace. This is equivalent to the minimal polynomial of T...

learning the random subspace method, also called attribute bagging or feature bagging, is an ensemble learning method that attempts to reduce the correlation...

mapped to the zero vector of the co-domain; the kernel is always a linear subspace of the domain. That is, given a linear map L : V → W between two vector...

if and only if all its coefficients are zero. Linear subspace A linear subspace or vector subspace W of a vector space V is a non-empty subset of V that...

dimension n is defined as the set of the vector lines (that is, vector subspaces of dimension one) in a vector space V of dimension n + 1. Equivalently...

Multilinear subspace learning is an approach for disentangling the causal factor of data formation and performing dimensionality reduction. The Dimensionality...

of a subnormal A if K' ⊂ K is a reducing subspace of B and H ⊂ K' , then K' = K. (A subspace is a reducing subspace of B if it is invariant under both...

i.e., non-orthogonal design of modules and interfaces. Orthogonality reduces testing and development time because it is easier to verify designs that...

elements of a vector space V {\displaystyle V} is the smallest linear subspace of V {\displaystyle V} that contains S . {\displaystyle S.} It is the set...

Hilbert space. At a deeper level, perpendicular projection onto a linear subspace plays a significant role in optimization problems and other aspects of...

is a group homomorphism. A representation is reducible if it contains a nontrivial G-invariant subspace, that is to say, all the matrices D ( a ) {\displaystyle...

mathematics, the commutator subspace of a two-sided ideal of bounded linear operators on a separable Hilbert space is the linear subspace spanned by commutators...

more extensive single-player mode than its predecessors, known as "The Subspace Emissary". This mode is a plot-driven and side-scrolling beat 'em up featuring...

Hermiticity, K n − 1 {\displaystyle {\mathcal {K}}^{n-1}} is an invariant subspace of A. To see that, consider any k ∈ K n − 1 {\displaystyle k\in {\mathcal...

theorem on complete reducibility: the case where a representation V {\displaystyle V} contains a nontrivial, irreducible, invariant subspace W {\displaystyle...

(}X\times \{0\}{\bigr )}\to v} . If X {\displaystyle X} is a non-empty compact subspace of Euclidean space, the cone on X {\displaystyle X} is homeomorphic to...

Mayer and Leopold Vietoris. The method consists of splitting a space into subspaces, for which the homology or cohomology groups may be easier to compute...

dimensional Euclidean space into invariant subspaces of A. Every Jordan block Ji corresponds to an invariant subspace Xi. Symbolically, we put C n = ⨁ i = 1...

non-Hermitian) matrices by constructing an orthonormal basis of the Krylov subspace, which makes it particularly useful when dealing with large sparse matrices...