Surjectivity

A map $f:A\to B$ (i.e., a function or linear transformation) is surjective (or onto) if for any $b\in B$, it is possible to find an element $a\in A$ such that $f(a)=b$. In other words, for every element in the codomain, the map is surjective if there is at least one element in the domain that maps to it.

A linear transformation $T:{\mathbb{R}}^m\to {\mathbb{R}}^n$ is surjective if there’s a pivot in every row after row reducing.

See also

• Injectivity
• Bijectivity