com.numericalmethod.suanshu.mathstructure

Interface HilbertSpace<H,F extends Field<F> & java.lang.Comparable<F>>

Type Parameters:

H - a Hilbert space

All Superinterfaces:

AbelianGroup<H>, BanachSpace<H,F>, java.io.Serializable, VectorSpace<H,F>

All Known Subinterfaces:

Vector

All Known Implementing Classes:

Basis, DenseVector, Gradient, ImmutableVector, SparseVector, SVEC

public interface HilbertSpace<H,F extends Field<F> & java.lang.Comparable<F>>
extends BanachSpace<H,F>

A Hilbert space is an inner product space, an abstract vector space in which distances and angles can be measured. It is also "complete", meaning that if a sequence of vectors is Cauchy, then it converges to some limit in the space.

See Also:

Wikipedia: Hilbert space

Method Summary

Modifier and Type	Method and Description
double	angle(H that) ∠ : H × H → F Inner product formalizes the geometrical notions such as the length of a vector and the angle between two vectors.
double	innerProduct(H that) <·,·> : H × H → F Inner product formalizes the geometrical notions such as the length of a vector and the angle between two vectors.

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

norm

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

innerProduct

double innerProduct(H that)

<·,·> : H × H → F

Inner product formalizes the geometrical notions such as the length of a vector and the angle between two vectors. It defines orthogonality between two vectors, where their inner product is 0.

Parameters:

that - the object to form an angle with this

Returns:

<this,that>

angle

double angle(H that)

∠ : H × H → F

Inner product formalizes the geometrical notions such as the length of a vector and the angle between two vectors. It defines orthogonality between two vectors, where their inner product is 0.

Parameters:

that - the object to form an angle with this

Returns:

the angle between this and that