Go to the previous, next section.

A vector_space is a set of vectors such that (1) if we add any two
vectors `x`

and `y`

in the space, their sum `x+y`

is also
in the space, and (2) if we multiply any vector `x`

in the space by
a scalar `c`

, then `cx`

is still in the space. The
`vector_space`

class is built using the `matrix`

(see section Matrices for Linear Algebra) class and the
fract_vector_list class (a list of `fract_vectors`

). The
vector space is represented either by a list independent vectors, or by
the column vectors of the matrix. Only one of the two representations
is stored at any given time. If the other representation is needed,
then it is recalculated. The class also contains an integer
`space`

that corresponds to the dimension of vector space; that is,
the maximum number of dimensions that this vector space could possibly
span. All basis vectors in the `fract_vector_list`

representation
must have `space`

elements. Alternatively, the matrix in the
`matrix`

representation must have `space`

rows.

- Basic Vector Space Functions: Standard vector space functions
- Vector Space Math Operations: Functions on vector spaces
- Vector Space Utilities: Utilities for manipulating vector spaces

Go to the previous, next section.