trait NormedVectorSpace[V, @specialized(Int, Long, Float, Double) F] extends VectorSpace[V, F] with MetricSpace[V, F]
A normed vector space is a vector space equipped with a function norm: V => F. The main constraint is that the norm
of a vector must be scaled linearly when the vector is scaled; that is norm(k *: v) == k.abs * norm(v).
Additionally, a normed vector space is also a MetricSpace, where distance(v, w) = norm(v - w), and so must obey
the triangle inequality.
An example of a normed vector space is R^n equipped with the euclidean vector length as the norm.
- Companion
- object
trait AdditiveCommutativeGroup[V]
trait AdditiveCommutativeMonoid[V]
trait AdditiveCommutativeSemigroup[V]
trait AdditiveGroup[V]
trait AdditiveMonoid[V]
trait AdditiveSemigroup[V]
trait Serializable
class Any
Value members
Abstract methods
Inherited methods
override
- Definition Classes
- AdditiveCommutativeGroup -> AdditiveCommutativeMonoid -> AdditiveCommutativeSemigroup -> AdditiveGroup -> AdditiveMonoid -> AdditiveSemigroup
- Inherited from
- AdditiveCommutativeGroup
Given a sequence of as, compute the sum.
Given a sequence of as, compute the sum.
- Inherited from
- AdditiveMonoid
override
- Definition Classes
- AdditiveGroup -> AdditiveMonoid -> AdditiveSemigroup
- Inherited from
- AdditiveGroup