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], AdditiveCommutativeGroup[V], AdditiveCommutativeMonoid[V], AdditiveCommutativeSemigroup[V], algebra.ring.AdditiveGroup[V], algebra.ring.AdditiveMonoid[V], algebra.ring.AdditiveSemigroup[V], Serializable, Serializable, Any
Known Subclasses
ArrayCoordinateSpace, CoordinateSpace, DistInnerProductSpace, DistNormedVectorSpace, DistVectorSpace, FieldAlgebra, InnerProductSpace, MapInnerProductSpace, MapVectorSpace, NormedVectorSpace, PolynomialOverField, SeqCoordinateSpace, SeqInnerProductSpace, SeqLpNormedVectorSpace, SeqMaxNormedVectorSpace, SeqVectorSpace
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Inherited
  1. VectorSpace
  2. Module
  3. AdditiveCommutativeGroup
  4. AdditiveCommutativeMonoid
  5. AdditiveCommutativeSemigroup
  6. AdditiveGroup
  7. AdditiveMonoid
  8. AdditiveSemigroup
  9. Serializable
  10. Serializable
  11. Any
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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: CommutativeGroup[V]

    Definition Classes
    AdditiveCommutativeGroup → AdditiveCommutativeMonoid → AdditiveCommutativeSemigroup → 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: algebra.Eq[V]): Boolean

    Definition Classes
    AdditiveMonoid

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

    Definition Classes
    AdditiveGroup

  12. def positiveSumN(a: V, n: Int): V

    Attributes
    protected[this]
    Definition Classes
    AdditiveSemigroup

  13. def sum(as: TraversableOnce[V]): V

    Definition Classes
    AdditiveMonoid

  14. def sumN(a: V, n: Int): V

    Definition Classes
    AdditiveGroup → AdditiveMonoid → AdditiveSemigroup

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

    Definition Classes
    Module

  16. def toString(): String

    Definition Classes
    Any

  17. def trySum(as: TraversableOnce[V]): Option[V]

    Definition Classes
    AdditiveMonoid → AdditiveSemigroup

Inherited from Module[V, F]

Inherited from AdditiveCommutativeGroup[V]

Inherited from AdditiveCommutativeMonoid[V]

Inherited from AdditiveCommutativeSemigroup[V]

Inherited from algebra.ring.AdditiveGroup[V]

Inherited from algebra.ring.AdditiveMonoid[V]

Inherited from algebra.ring.AdditiveSemigroup[V]

Inherited from Serializable

Inherited from Serializable

Inherited from Any

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