written as , or sometimes, ; the number is called the nullity of and written as or . If and are finite-dimensional, bases have been chosen and is represented by the matrix , then the rank and nullity of are equal to the rank and nullity of the matrix , respectively.

Cokernel

A subtler invariant of a linear transformation is the ''co''kernel, which is defined as

This is the dual notion to the kernel: just as the kernel is a subspace

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