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@jemoka / Jemoka Knowledge Base / wiki/concepts/surjectivity.md
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--- 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 \(W\). “onto” “For any possible output, \(w \in W\) for \(T \in \mathcal{L}(V,W)\), there is at LEAST one input \(T\) that maps \(Tv \to w\). " \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