Definitions for "Onto"
Keywords:  codomain, subspace, pivot, null, merely
linear transformation, T, is onto if its range is all of its codomain, not merely a subspace. Thus, for any vector , the equation T() = has at least one solution (is consistent). The linear transformation T is 1-to-1 if and only if the null space of its corresponding matrix has only the zero vector in its null space. Equivalently, a linear transformation is 1-to-1 if and only if its corresponding matrix has no non-pivot columns.
Keywords:  prep, top, see
On the top of; upon; on. See On to, under On, prep.
Keywords:  map, function
A function f is said to map A onto B if for every b in B, there is some a in A such f(a)=b.
Keywords:  function
A function f from X to Y where f(X)=Y.