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], Any
Known Subclasses
CoordinateSpace, FieldAlgebra, InnerProductSpace, NormedVectorSpace, PolynomialEuclideanRing, DistInnerProductSpace, DistNormedVectorSpace, DistVectorSpace, ArrayCoordinateSpace, MapInnerProductSpace, MapVectorSpace, SeqCoordinateSpace, SeqInnerProductSpace, SeqLpNormedVectorSpace, SeqMaxNormedVectorSpace, SeqVectorSpace
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Inherited
  1. VectorSpace
  2. Module
  3. AdditiveAbGroup
  4. AdditiveCMonoid
  5. AdditiveCSemigroup
  6. AdditiveGroup
  7. AdditiveMonoid
  8. AdditiveSemigroup
  9. Any
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Visibility
  1. Public
  2. All

Abstract Value Members

  1. abstract def getClass(): Class[_]
    Definition Classes
    Any
  2. abstract def negate(x: V): V
    Definition Classes
    AdditiveGroup
  3. abstract def plus(x: V, y: V): V
    Definition Classes
    AdditiveSemigroup
  4. implicit abstract def scalar: Field[F]
    Definition Classes
    VectorSpace → Module
  5. abstract def timesl(r: F, v: V): V
    Definition Classes
    Module
  6. abstract def zero: V
    Definition Classes
    AdditiveMonoid

Concrete Value Members

  1. final def !=(arg0: Any): Boolean
    Definition Classes
    Any
  2. final def ##(): Int
    Definition Classes
    Any
  3. final def ==(arg0: Any): Boolean
    Definition Classes
    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 divr(v: V, f: F): V
  7. def equals(arg0: Any): Boolean
    Definition Classes
    Any
  8. def hashCode(): Int
    Definition Classes
    Any
  9. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  10. def isZero(a: V)(implicit ev: Eq[V]): Boolean

    Tests if a is zero.

    Tests if a is zero.

    Definition Classes
    AdditiveMonoid
  11. def minus(x: V, y: V): V
    Definition Classes
    AdditiveGroup
  12. def sum(as: TraversableOnce[V]): V

    Given a sequence of as, sum them using the monoid and return the total.

    Given a sequence of as, sum them using the monoid and return the total.

    Definition Classes
    AdditiveMonoid
  13. def sumOption(as: TraversableOnce[V]): Option[V]

    Given a sequence of as, sum them using the semigroup and return the total.

    Given a sequence of as, sum them using the semigroup and return the total.

    If the sequence is empty, returns None. Otherwise, returns Some(total).

    Definition Classes
    AdditiveSemigroup
  14. def sumn(a: V, n: Int): V

    Return a added with itself n times.

    Return a added with itself n times.

    Definition Classes
    AdditiveGroup → AdditiveMonoid → AdditiveSemigroup
  15. def sumnAboveOne(a: V, n: Int): V
    Attributes
    protected
    Definition Classes
    AdditiveSemigroup
  16. def timesr(v: V, r: F): V
    Definition Classes
    Module
  17. def toString(): String
    Definition Classes
    Any

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 Any

Ungrouped