Surjective

Let $$V_1$$ and $$V_2$$ be normed spaces and let $$T$$ be an operator $$T:V_1\to V_2$$. Then, $$T$$ is surjective if for each $$\mathbf{w} \in V_2$$ there exists $$\mathbf{v} \in V_1$$ such that $$T\mathbf{v} = w$$.

If $$T$$ is a matrix, this means that it has full row rank. A surjective matrix $$T$$ is also called onto.

See also injective and bijective.