33.5 Subspaces and Parent Spaces

The concept described in this section is essentially the same as the concept of parent groups and subgroups (see More about Groups and Subgroups).

(The section should be moved to chapter Vector Spaces, but for general vector spaces the concept does not yet apply.)

Every row space U is either constructed as subspace of an existing space V, for example using Subspace Subspace, or it is not.

In the latter case the space is called a parent space, in the former case V is called the parent of U.

One can only form sums of subspaces of the same parent space, form quotient spaces only for spaces with same parent, and cosets v + U only for representatives v in the parent of U.

Parent( V ) :

returns the parent space of the row space V,

IsParent( V ) :

returns true if the row space V is a parent space, and false otherwise.

See AsSubspace, AsSpace for conversion functions.

Previous Up Top Next
Index