subspaces's Usage Examples:

Two vector subspaces, A and B, of an inner product space V, are called orthogonal subspaces if each vector in A is orthogonal to.

{E}}} ) has two sorts of subspaces: its Euclidean subspaces and its linear subspaces.

Linear subspaces are Euclidean subspaces and a Euclidean subspace.

linear subspaces: the zero vector space consisting of the zero vector alone and the entire vector space itself.

These are called the trivial subspaces of.

words, all the examples found of operators with no non-trivial invariant subspaces act on Banach spaces which are not separable Hilbert spaces).

the column space, and the left null space of A are the four fundamental subspaces associated to the matrix A.

space which contains the given Hilbert spaces as mutually orthogonal subspaces.

Grassmannian Gr(k, V) is a space that parameterizes all k-dimensional linear subspaces of the n-dimensional vector space V.

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

{\displaystyle k^{n}} can be decomposed as the direct sum of Krylov subspaces.

Krylov subspaces are used in algorithms for finding approximate solutions to high-dimensional.

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.

Flats are the affine subspaces of Euclidean spaces, which means that they are similar to linear subspaces, except that they need not pass through.

topological space whose topology is coherent with the family of all compact subspaces.

It can be characterized either as the intersection of all linear subspaces that contain S, or as the set of linear combinations of elements of S.

immediate examples of invariant subspaces.

Certainly V itself, and the subspace {0}, are trivially invariant subspaces for every linear operator T : V.

vector space and M {\displaystyle M} and N {\displaystyle N} are vector subspaces of X {\displaystyle X} then X {\displaystyle X} is the algebraic direct.

Linear subspaces, in contrast, always contain the origin of the vector space.

p\neq 2} and c 0 {\displaystyle c_{0}} (see Sequence space) have closed subspaces that do not have the approximation property.

vector subspace M of X is called maximal if M ⊊ X, but there are no vector subspaces N satisfying M ⊊ N ⊊ X.

SUBCLU can find clusters in axis-parallel subspaces, and uses a bottom-up, greedy strategy to remain efficient.

Synonyms:

topological space; mathematical space;