dev.nm.algebra.structure

Interface BanachSpace<B,F extends Field<F> & Comparable<F>>

All Superinterfaces:

AbelianGroup<B>, VectorSpace<B,F>

All Known Subinterfaces:

HilbertSpace<H,F>, Vector

All Known Implementing Classes:

Basis, CombinedVectorByRef, DenseVector, Gradient, ImmutableVector, SparseVector, SubVectorRef, SVEC

public interface BanachSpace<B,F extends Field<F> & Comparable<F>>
extends VectorSpace<B,F>

A Banach space, B, is a complete normed vector space such that every Cauchy sequence (with respect to the metric d(x, y) = |x - y|) in B has a limit in B.

See Also:

Wikipedia: Banach space

Method Summary

Modifier and Type	Method and Description
double	norm() |⋅| : B → F norm assigns a strictly positive length or size to all vectors in the vector space, other than the zero vector.

Methods inherited from interface dev.nm.algebra.structure.VectorSpace

scaled

Methods inherited from interface dev.nm.algebra.structure.AbelianGroup

add, minus, opposite, ZERO

Method Detail

norm

double norm()

|⋅| : B → F

norm assigns a strictly positive length or size to all vectors in the vector space, other than the zero vector.

Returns:

|this|

See Also:

Wikipedia: Norm (mathematics)