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 finite graph with vertex
set 
,
 |
where 
counts the connected components of the spanning subgraph with edge
set 
, including isolated
vertices.
