A binary matroid is a matroid representable by the columns of a matrix over the two-element finite
field 
.
A set of column labels is independent in the matroid
precisely when the corresponding columns are linearly
independent over 
.
Every graphic matroid is binary. For example, the columns of the incidence matrix of a graph,
interpreted over 
,
represent its graphic matroid. Binary representability
depends on the field, not merely on whether the entries
of a representing matrix are 0 and 1.
