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], AdditiveCMonoid[V], AdditiveCSemigroup[V], AdditiveGroup[V], AdditiveMonoid[V], AdditiveSemigroup[V], AnyRef, Any
Known Subclasses
ArrayCoordinateSpace, CoordinateSpace, DistInnerProductSpace, DistNormedVectorSpace, DistVectorSpace, FieldAlgebra, InnerProductSpace, MapInnerProductSpace, MapVectorSpace, NormedVectorSpace, PolynomialEuclideanRing, SeqCoordinateSpace, SeqInnerProductSpace, SeqLpNormedVectorSpace, SeqMaxNormedVectorSpace, SeqVectorSpace
Ordering
  1. Alphabetic
  2. By inheritance
Inherited
  1. VectorSpace
  2. Module
  3. AdditiveAbGroup
  4. AdditiveCMonoid
  5. AdditiveCSemigroup
  6. AdditiveGroup
  7. AdditiveMonoid
  8. AdditiveSemigroup
  9. AnyRef
  10. Any
  1. Hide All
  2. Show all
Learn more about member selection
Visibility
  1. Public
  2. All

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: Any): Boolean

    Definition Classes
    AnyRef → Any

  2. final def ##(): Int

    Definition Classes
    AnyRef → Any

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

    Definition Classes
    AnyRef → Any

  4. def additive: AbGroup[V]

    Definition Classes
    AdditiveAbGroup → AdditiveCMonoid → AdditiveCSemigroup → AdditiveGroup → AdditiveMonoid → AdditiveSemigroup

  5. final def asInstanceOf[T0]: T0

    Definition Classes
    Any

  6. def clone(): AnyRef

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

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

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

    Definition Classes
    AnyRef

  9. def equals(arg0: Any): Boolean

    Definition Classes
    AnyRef → Any

  10. def finalize(): Unit

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

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

    Definition Classes
    AnyRef → Any

  12. def hashCode(): Int

    Definition Classes
    AnyRef → Any

  13. final def isInstanceOf[T0]: Boolean

    Definition Classes
    Any

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

    Definition Classes
    AdditiveGroup

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

    Definition Classes
    AnyRef

  16. final def notify(): Unit

    Definition Classes
    AnyRef

  17. final def notifyAll(): Unit

    Definition Classes
    AnyRef

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

    Definition Classes
    AnyRef

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

    Definition Classes
    Module

  20. def toString(): String

    Definition Classes
    AnyRef → Any

  21. final def wait(): Unit

    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

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

    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

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

    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

Inherited from Module[V, F]

Inherited from AdditiveAbGroup[V]

Inherited from AdditiveCMonoid[V]

Inherited from AdditiveCSemigroup[V]

Inherited from AdditiveGroup[V]

Inherited from AdditiveMonoid[V]

Inherited from AdditiveSemigroup[V]

Inherited from AnyRef

Inherited from Any

Ungrouped