Package dev.nm.algebra.structure
Interface HilbertSpace<H,F extends Field<F> & Comparable<F>>
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- Type Parameters:
H- a Hilbert space
- All Superinterfaces:
AbelianGroup<H>,BanachSpace<H,F>,VectorSpace<H,F>
- All Known Subinterfaces:
Vector
- All Known Implementing Classes:
Basis,CombinedVectorByRef,DenseVector,Gradient,ImmutableVector,SparseVector,SubVectorRef,SVEC
public interface HilbertSpace<H,F extends Field<F> & 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
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Method Summary
All Methods Instance Methods Abstract Methods Modifier and Type Method Description doubleangle(H that)∠ : H × H → FdoubleinnerProduct(H that)<⋅,⋅> : H × H → F-
Methods inherited from interface dev.nm.algebra.structure.AbelianGroup
add, minus, opposite, ZERO
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Methods inherited from interface dev.nm.algebra.structure.BanachSpace
norm
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Methods inherited from interface dev.nm.algebra.structure.VectorSpace
scaled
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Method Detail
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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 withthis- Returns:
- <this,that>
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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
thisandthat
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