A row space is a vector space (see chapter Vector Spaces), whose elements are row vectors, that is, lists of elements in a common field.
Note that for a row space V over the field F necessarily the characteristic of F is the same as the characteristic of the vectors in V. Furthermore at the moment the field F must contain the field spanned by all the elements in vectors of V, since in many computations vectors are normed, that is, divided by their first nonzero entry.
The implementation of functions for these spaces and their elements uses the well-known linear algebra methods, such as Gaussian elimination, and many functions delegate the work to functions for matrices, e.g., a basis of a row space can be computed by performing Gaussian elimination to the matrix formed by the list of generators. Thus in a sense, a row space in GAP is nothing but a GAP object that knows about the interpretation of a matrix as a generating set, and that knows about the functions that do the work.
Row spaces are constructed using RowSpace RowSpace, full row spaces can
also be constructed by F ^ n, for a field F and a positive integer
n.
The zero element of a row space V in GAP is not necessarily stored in
the row space record. If necessary, it can be computed using Zero( V ).
The generators component may contain zero vectors, so no function should
expect a generator to be nonzero.
See Operations for Row Spaces and Functions for Row Spaces for an overview of applicable operators and functions, and Row Space Records for details of the implementation.
GAP 3.4.4