Note that if is a subspace of , then this (applied to the canonical mapping ) says that
where denotes codimension.
An alternative way of stating the rank-nullity theorem is by saying that if
is a short exact sequence of vector spaces, then
In fact, if
is an exact sequence of vector spaces, then
that is, the sum of the dimensions of even-numbered terms is the same as the sum of the dimensions of the odd-numbered terms.
|Date of creation||2013-03-22 16:35:40|
|Last modified on||2013-03-22 16:35:40|
|Last modified by||yark (2760)|