---
title: "surjectivity"
type: concept
related: [Surjectivity, Range]
source: https://www.jemoka.com/posts/kbhsurjectivity/
confidence: high
status: active
---

A function \(T: V\to W\) is surjective if its range equals its codomain \(W\). &ldquo;onto&rdquo;
&ldquo;For any possible output, \(w \in W\) for \(T \in \mathcal{L}(V,W)\), there is at LEAST one input \(T\) that maps \(Tv \to w\). &quot;
\begin{equation} \forall w \in W, \exists v \in V:Tv=W \end{equation}
map to bigger space is not surjective See map to bigger space is not surjective
