What is "corank"

n. (context mathematics English) (rfdef: English)

In mathematics, corank may refer to any of several related concepts, complementary to the concept of the rank of a mathematical object:

• The corank of an m × n matrix is m − r where r is the rank of the matrix. Equivalently, by the fundamental theorem of linear algebra, it is the dimension of the left nullspace of the matrix.
• 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.
• For a matroid with n elements and matroid rank r, the corank or nullity of the matroid is n − r. 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.