Editing Row and column spaces (section)

===Relation to coimage===
If {{mvar|V}} and {{mvar|W}} are [[vector spaces]], then the [[kernel (linear algebra)|kernel]] of a [[linear transformation]] {{math|''T'': ''V'' → ''W''}} is the set of vectors {{math|'''v''' ∈ ''V''}} for which {{math|1=''T''('''v''') = '''0'''}}.  The kernel of a linear transformation is analogous to the null space of a matrix.

If {{mvar|V}} is an [[inner product space]], then the orthogonal complement to the kernel can be thought of as a generalization of the row space.  This is sometimes called the [[coimage]] of {{mvar|T}}.  The transformation {{mvar|T}} is one-to-one on its coimage, and the coimage maps [[isomorphism|isomorphically]] onto the [[image (mathematics)|image]] of {{mvar|T}}.

When {{mvar|V}} is not an inner product space, the coimage of {{mvar|T}} can be defined as the [[quotient space (linear algebra)|quotient space]] {{math|''V'' / ker(''T'')}}.