Editing Matroid (section)

===Sums and unions===
Let ''M'' be a matroid with an underlying set of elements ''E'', and let ''N'' be another matroid on an underlying set ''F''.
The ''direct sum'' of matroids ''M'' and ''N'' is the matroid whose underlying set is the [[disjoint union]] of ''E'' and ''F'', and whose independent sets are the disjoint unions of an independent set of ''M'' with an independent set of ''N''.

The ''union'' of ''M'' and ''N'' is the matroid whose underlying set is the union (not the disjoint union) of ''E'' and ''F'', and whose independent sets are those subsets that are the union of an independent set in ''M'' and one in ''N''. Usually the term "union" is applied when ''E'' = ''F'', but that assumption is not essential.  If ''E'' and ''F'' are disjoint, the union is the direct sum.