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6.4: Homomorphisms

  • Page ID
    274
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    It should be mentioned that linear maps between vector spaces are also called vector space homomorphisms. Instead of the notation \( \mathcal{L} (V,W) \), one often sees the convention

    \[ \mathrm{Hom}_\mathbb{F} (V,W) = \{ T:V \to W \mid \text{ T is linear} \}. \]

    A homomorphism \(T:V \to W \) is also often called

    1. Monomorphism iff \(T \) is injective;
    2. Epimorphism iff \(T \) is surjective;
    3. Isomorphism iff \(T \) is bijective;
    4. Endomorphism iff \(V=W \);
    5. Automorphism iff \(V=W \) and \(T \) is bijective.


    This page titled 6.4: Homomorphisms is shared under a not declared license and was authored, remixed, and/or curated by Isaiah Lankham, Bruno Nachtergaele, & Anne Schilling.

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