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Math Help - Vector Isomorphism

  1. #1
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    Vector Isomorphism

    Let L:V --> be an isomorphism of vector space V onto vector space W. Show that L(v-w)= L(v) - L(w)

    If v = [a1, a2, a3] and w = [b1, b2, b3]

    L(v - w) = L(a1 - b1, a2 - b2, a3 - b3)

    How do I take the next step in proving that L(v) - L(w)? It seems too simple to just separate it into L(a1, a2, a3) - L(b1, b2, b3) which would then equal L(v) - L(w). Am I missing a step, or is it that simple? Thanks!
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  2. #2
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    Quote Originally Posted by Brokescholar View Post
    Let L:V --> be an isomorphism of vector space V onto vector space W. Show that L(v-w)= L(v) - L(w)
    L(\bold{v}-\bold{w}) = L(\bold{v} + (-1)\bold{w}) = L(\bold{v}) + L(-\bold{w}) = L(\bold{v}) - L(\bold{w})
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