linear subspace in a sentence

Examples

1. The displacement vectors for that affine space are the solutions of the corresponding " homogeneous " linear system, which is a linear subspace.
2. In mathematics, the "'Grassmannian "'is a space which parameterizes all linear subspaces of a vector space of given dimension.
3. Grassmannians by definition are the parameter spaces for linear subspaces, of a given dimension, in a given vector space " W ".
4. If is the direct sum of two closed linear subspaces and, then the dual of is isomorphic to the direct sum of the duals of and.
5. The linear subspace where these equations are satisfied is one of the constraint spaces, say " A ", used by the difference map.
6. A densely defined operator from a complex Hilbert space to itself is a linear operator whose domain is a dense linear subspace of and whose values lies in.
7. Linear subspace learning algorithms are traditional dimensionality reduction techniques that represent input data as vectors and solve for an optimal linear mapping to a lower-dimensional space.
8. Formally, the real projective line is defined as the space of all one-dimensional linear subspaces of a two-dimensional vector space over the reals.
9. Using the Hausdorff maximal principle and the fact that in a complete inner product space orthogonal projection onto linear subspaces is well-defined, one may also show that
10. Both are dense linear subspaces, but their intersection is a line-the constant functions .-- a 19 : 17, 11 October 2010 ( UTC)