org.ojalgo.algebra

Interface VectorSpace<V,F extends Number>

Type Parameters:

V - The vector type

F - The scalar type

All Superinterfaces:

Group, Group.Additive<V>, Operation, Operation.Addition<V>, ScalarOperation, ScalarOperation.Multiplication<V,F>

All Known Subinterfaces:

DecompositionStore<N>, MatrixStore<N>, NormedVectorSpace<V,F>, PhysicalStore<N>, Scalar<N>, Tensor<N>

All Known Implementing Classes:

BigScalar, ComplexMatrix, ComplexNumber, ComplexNumber.Normalised, ExactDecimal, GenericDenseStore, Money, PrimitiveDenseStore, PrimitiveMatrix, PrimitiveScalar, Quaternion, Quaternion.Versor, QuaternionMatrix, RationalMatrix, RationalNumber, RawStore, SparseStore

public interface VectorSpace<V,F extends Number>
extends Group.Additive<V>, ScalarOperation.Multiplication<V,F>

A vector space is a set of objects called vectors, where a vector is a tuple of fields/scalars/numbers. Each vector space has two operations: vector addition and scalar multiplication. Eight axioms must be satisfied. The first four are the group axioms of the additive group of vectors. The remaining four relates to scalar multiplication, and are:

• Compatibility of scalar multiplication with field multiplication: a(bV) = (ab)V
• Identity element of scalar multiplication: 1V = V, where 1 denotes the multiplicative identity of the field.
• Distributivity of scalar multiplication with respect to vector addition: a(U + V) = aU + aV
• Distributivity of scalar multiplication with respect to field addition: (a + b)V = aV + bV

To enable the use of existing Java classes as scalars this interface declares the scalar type to be a subclass of Number rather than an implementation of Field.

Any field is also a vector space in itself.

Author:

apete

See Also:

Group.Additive, Field, Vector space, Examples of vector spaces

Nested Class Summary

Nested classes/interfaces inherited from interface org.ojalgo.algebra.Group

Group.Additive<S>, Group.Multiplicative<S>

Nested classes/interfaces inherited from interface org.ojalgo.algebra.Operation

Operation.Addition<T>, Operation.Division<T>, Operation.Multiplication<T>, Operation.Subtraction<T>

Nested classes/interfaces inherited from interface org.ojalgo.algebra.ScalarOperation

ScalarOperation.Addition<T,N extends Number>, ScalarOperation.Division<T,N extends Number>, ScalarOperation.Multiplication<T,N extends Number>, ScalarOperation.Subtraction<T,N extends Number>

Method Summary

Modifier and Type	Method and Description
V	conjugate() This method will (most likely) be moved to some other interface in the future! Just have to figure out where it fits...

Methods inherited from interface org.ojalgo.algebra.Group.Additive

negate

Methods inherited from interface org.ojalgo.algebra.Operation.Addition

add

Methods inherited from interface org.ojalgo.algebra.ScalarOperation.Multiplication

multiply, multiply

Method Detail

conjugate

V conjugate()

This method will (most likely) be moved to some other interface in the future! Just have to figure out where it fits...

The conjugate transpose of a matrix and/or the conjugate of a scalar/field like ComplexNumber or Quaternion.

The conjugate transpose of a real matrix is simply its transpose.