The type of scalars in this vector space.
The type of scalars in this vector space.
The type of vectors in this vector space.
The type of vectors in this vector space.
A vector in this vector space.
Returns the scalar set of this vector space.
Returns the scalar set of this vector space.
Returns a new vector with the given coordinates.
Returns the dimension of this vector space.
Returns the additive identity of this vector space.
Returns the additive identity of this vector space.
An abstract N-dimensional vector space over a ring. Vector addition associates and commutes, and scalar multiplication associates, commutes, and distributes over vector addition and scalar addition. Vector addition and scalar multiplication both have an identity element, and every vector has an additive inverse. Every vector space is an affine space over itself. To the extent practicable, the following axioms should hold.
Axioms for vector addition:
this
, then their sum 𝐮 + 𝐯 is also a vector inthis
.this
.this
.this
has a vectorzero
such thatzero
+ 𝐯 == 𝐯 for every vector 𝐯 inthis
.this
corresponds a vector -𝐯 inthis
such that 𝐯 + (-𝐯) ==zero
.Axioms for scalar multiplication:
this
and 𝐯 is a vector inthis
, then their product 𝑎 *: 𝐯 is also a vector inthis
.this
.Scalar
has an elementunit
such thatunit
*: 𝐯 == 𝐯 for every vector 𝐯 inthis
.Distributive laws:
this
.this
.0.1
0.0