fifth-postulate/gaussian-elimination/1.0.0

Algebra.VectorSpace

Provide a VectorSpace.

A VectorSpace is

a set whose elements, often called vectors, can be added together and multiplied ("scaled") by numbers called scalars

Type

The VectorSpace type.

It is parameterized over the elements its vectors contains.

Creation

span : Field a -> List (Vector a) -> VectorSpace a

Create the VectorSpace that is spanned by the list of vectors.

The empty VectorSpace.

Equality

equals : Field a -> VectorSpace a -> VectorSpace a -> Bool

Determines if two VectorSpaces are the same linear spaces.

Operation

add : Field a -> Vector a -> VectorSpace a -> VectorSpace a

Add a Vector to the basis of the VectorSpace.

contains : Field a -> Vector a -> VectorSpace a -> Bool

Determinis if a Vector is contiained in the VectorSpace

The intersection of two VectorSpaces.

This is formed by the linear space of all the vectors that are contained in both VectorSpaces.

all : (Vector Finite -> b) -> Field Finite -> VectorSpace Finite -> List b

Iterate over all Vectors in this VectorSpace.

Apply a transformation on each Vector and return the result as a list.