Vector matroid

Vector matroid --- матроид векторный.

Consider an [math]\displaystyle{ r \times n }[/math] matrix [math]\displaystyle{ A }[/math] over a field [math]\displaystyle{ F }[/math] with its columns labeled by [math]\displaystyle{ \{1,2, \ldots, n\} }[/math]. Define [math]\displaystyle{ E }[/math] as the set of column labels and [math]\displaystyle{ {\mathcal I} }[/math] as subsets of column labels that correspond to linearly independent sets of columns in the vector space [math]\displaystyle{ V(r,F) }[/math]. Then [math]\displaystyle{ {\mathcal I} }[/math] satisfies the three postulates and the resulting matroid, denoted by [math]\displaystyle{ M[A] }[/math], is called the vector matroid of [math]\displaystyle{ A }[/math].