com.numericalmethod.suanshu.mathstructure
Interface BanachSpace<B,F extends Field<F> & java.lang.Comparable<F>>

All Superinterfaces:

AbelianGroup<B>, VectorSpace<B,F>

All Known Subinterfaces:

HilbertSpace<H,F>, Vector

All Known Implementing Classes:

Basis, DenseVector, ImmutableVector, SparseVector

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

This interface represents a Banach space.

A Banach space is a complete normed vector space. A Banach space is a vector space V with a norm ||·|| 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

double

norm() ||·|| : B → F norm is a function that assigns a strictly positive length or size to all vectors in a vector space, other than the zero vector.

Methods inherited from interface com.numericalmethod.suanshu.mathstructure.VectorSpace

scaled

Methods inherited from interface com.numericalmethod.suanshu.mathstructure.AbelianGroup

add, minus, opposite, ZERO

Method Detail

norm

double norm()

||·|| : B → F

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

Returns:

||this||

See Also:

Wikipedia: Norm (mathematics)