The matroid rank of a subset 
of a matroid is the maximum number
of elements of an independent subset of 
. If 
is the family of independent sets, its rank function is
 |
The rank of the entire matroid is the common number of elements of its matroid bases.
For a matroid represented by columns of a matrix, 
is the matrix
rank of the columns labeled by 
. For the graphic matroid
of a graph with vertex set 
,
 |
where 
counts the connected components of the spanning
subgraph with edge set 
, including isolated
vertices.
