Corank

In mathematics, corank is complementary to the concept of the rank of a mathematical object, and may refer to the dimension of the left nullspace of a matrix, the dimension of the cokernel of a linear transformation of a vector space, or the number of elements of a matroid minus its rank. 
Left nullspace of a matrix.
The corank of an formula_1 matrix is formula_2 where formula_3 is the rank of the matrix. It is the dimension of the left nullspace and of the cokernel of the matrix.
Cokernel of a linear transformation.
Generalizing matrices to linear transformations of vector spaces, the corank of a linear transformation is the dimension of the cokernel of the transformation, which is the quotient of the codomain by the image of the transformation.
Matroid.
For a matroid with formula_4 elements and matroid rank formula_3, the corank or nullity of the matroid is formula_6. In the case of linear matroids this coincides with the matrix corank. In the case of graphic matroids the corank is also known as the circuit rank or cyclomatic number.