VectorSpace

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

ArrayCoordinateSpace, CoordinateSpace, DistInnerProductSpace, DistNormedVectorSpace, DistVectorSpace, FieldAlgebra, InnerProductSpace, MapInnerProductSpace, MapVectorSpace, NormedVectorSpace, PolynomialEuclideanRing, SeqCoordinateSpace, SeqInnerProductSpace, SeqLpNormedVectorSpace, SeqMaxNormedVectorSpace, SeqVectorSpace

Abstract Value Members

abstract def getClass(): Class[_]

Definition Classes
Any
abstract def negate(x: V): V

Definition Classes
AdditiveGroup
abstract def plus(x: V, y: V): V

Definition Classes
AdditiveSemigroup
implicit abstract def scalar: Field[F]

Definition Classes
VectorSpace → Module
abstract def timesl(r: F, v: V): V

Definition Classes
Module
abstract def zero: V

Definition Classes
AdditiveMonoid

Concrete Value Members

final def !=(arg0: Any): Boolean

Definition Classes
Any
final def ##(): Int

Definition Classes
Any
final def ==(arg0: Any): Boolean

Definition Classes
Any
def additive: AbGroup[V]

Definition Classes
AdditiveAbGroup → AdditiveCMonoid → AdditiveCSemigroup → AdditiveGroup → AdditiveMonoid → AdditiveSemigroup
final def asInstanceOf[T0]: T0

Definition Classes
Any
def divr(v: V, f: F): V
def equals(arg0: Any): Boolean

Definition Classes
Any
def hashCode(): Int

Definition Classes
Any
final def isInstanceOf[T0]: Boolean

Definition Classes
Any
def isZero(a: V)(implicit ev: Eq[V]): Boolean

Tests if a is zero.
Tests if a is zero.

Definition Classes
AdditiveMonoid
def minus(x: V, y: V): V

Definition Classes
AdditiveGroup
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
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
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
def sumnAboveOne(a: V, n: Int): V

Attributes
protected
Definition Classes
AdditiveSemigroup
def timesr(v: V, r: F): V

Definition Classes
Module
def toString(): String

Definition Classes
Any

Related Docs: object VectorSpace | package algebra

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

Abstract Value Members

abstract def getClass(): Class[_]

abstract def negate(x: V): V

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

implicit abstract def scalar: Field[F]

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

abstract def zero: V

Concrete Value Members

final def !=(arg0: Any): Boolean

final def ##(): Int

final def ==(arg0: Any): Boolean

def additive: AbGroup[V]

final def asInstanceOf[T0]: T0

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

def equals(arg0: Any): Boolean

def hashCode(): Int

final def isInstanceOf[T0]: Boolean

def isZero(a: V)(implicit ev: Eq[V]): Boolean

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

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

def sumOption(as: TraversableOnce[V]): Option[V]

def sumn(a: V, n: Int): V

def sumnAboveOne(a: V, n: Int): V

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

def toString(): String

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