spire.algebra

VectorSpace

trait VectorSpace[V, F] extends Module[V, F]

A vector space is a group V that can be multiplied by scalars in F that lie in a field. Scalar multiplication must distribute over vector addition (x *: (v + w) === x *: v + x *: w) and scalar addition ((x + y) *: v === x *: v + y *: v). Scalar multiplication by 1 in F is an identity function (1 *: v === v). Scalar multiplication is "associative" (x *: y *: v === (x * y) *: v).

Linear Supertypes
Module[V, F], AdditiveAbGroup[V], AdditiveGroup[V], AdditiveMonoid[V], AdditiveSemigroup[V], AnyRef, Any
Known Subclasses
ArrayCoordinateSpace, CoordinateSpace, FieldAlgebra, InnerProductSpace, MapInnerProductSpace, MapVectorSpace, NormedVectorSpace, SeqCoordinateSpace, SeqInnerProductSpace, SeqLpNormedVectorSpace, SeqMaxNormedVectorSpace, SeqVectorSpace
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Inherited
  1. VectorSpace
  2. Module
  3. AdditiveAbGroup
  4. AdditiveGroup
  5. AdditiveMonoid
  6. AdditiveSemigroup
  7. AnyRef
  8. Any
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Abstract Value Members

  1. abstract def negate(x: V): V

    Definition Classes
    AdditiveGroup

  2. abstract def plus(x: V, y: V): V

    Definition Classes
    AdditiveSemigroup

  3. implicit abstract def scalar: Field[F]

    Definition Classes
    VectorSpace → Module

  4. abstract def timesl(r: F, v: V): V

    Definition Classes
    Module

  5. abstract def zero: V

    Definition Classes
    AdditiveMonoid

Concrete Value Members

  1. final def !=(arg0: AnyRef): Boolean

    Definition Classes
    AnyRef

  2. final def !=(arg0: Any): Boolean

    Definition Classes
    Any

  3. final def ##(): Int

    Definition Classes
    AnyRef → Any

  4. final def ==(arg0: AnyRef): Boolean

    Definition Classes
    AnyRef

  5. final def ==(arg0: Any): Boolean

    Definition Classes
    Any

  6. def additive: AbGroup[V]

    Definition Classes
    AdditiveAbGroup → AdditiveGroup → AdditiveMonoid → AdditiveSemigroup

  7. final def asInstanceOf[T0]: T0

    Definition Classes
    Any

  8. def clone(): AnyRef

    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

  9. def divr(v: V, f: F): V

  10. final def eq(arg0: AnyRef): Boolean

    Definition Classes
    AnyRef

  11. def equals(arg0: Any): Boolean

    Definition Classes
    AnyRef → Any

  12. def finalize(): Unit

    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( classOf[java.lang.Throwable] )

  13. final def getClass(): Class[_]

    Definition Classes
    AnyRef → Any

  14. def hashCode(): Int

    Definition Classes
    AnyRef → Any

  15. final def isInstanceOf[T0]: Boolean

    Definition Classes
    Any

  16. def minus(x: V, y: V): V

    Definition Classes
    AdditiveGroup

  17. final def ne(arg0: AnyRef): Boolean

    Definition Classes
    AnyRef

  18. final def notify(): Unit

    Definition Classes
    AnyRef

  19. final def notifyAll(): Unit

    Definition Classes
    AnyRef

  20. final def synchronized[T0](arg0: ⇒ T0): T0

    Definition Classes
    AnyRef

  21. def timesr(v: V, r: F): V

    Definition Classes
    Module

  22. def toString(): String

    Definition Classes
    AnyRef → Any

  23. final def wait(): Unit

    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

  24. final def wait(arg0: Long, arg1: Int): Unit

    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

  25. final def wait(arg0: Long): Unit

    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

Inherited from Module[V, F]

Inherited from AdditiveAbGroup[V]

Inherited from AdditiveGroup[V]

Inherited from AdditiveMonoid[V]

Inherited from AdditiveSemigroup[V]

Inherited from AnyRef

Inherited from Any

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