com.numericalmethod.suanshu.mathstructure

Interface BanachSpace<B,F extends Field<F> & java.lang.Comparable<F>>

All Superinterfaces:

AbelianGroup<B>, java.io.Serializable, VectorSpace<B,F>

All Known Subinterfaces:

HilbertSpace<H,F>, Vector

All Known Implementing Classes:

Basis, DenseVector, Gradient, ImmutableVector, SparseVector, SVEC

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