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Math Help - Isomorpshims

  1. #1
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    Isomorpshims

    Let R^n={(a1,a2,....,an)| a_i in R}. Show that the mapping phi : (a1,a2,...,an) -> (-a1,-a2,....,-an) is an automorphism of the group R^n.
    under component wise addition.
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  2. #2
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    Quote Originally Posted by Juancd08 View Post
    Let R^n={(a1,a2,....,an)| a_i in R}. Show that the mapping phi : (a1,a2,...,an) -> (-a1,-a2,....,-an) is an automorphism of the group R^n.
    under component wise addition.
    You need to show \phi: \mathbb{R}^n \to \mathbb{R}^n is a bijective.
    And \phi(\bold{a}+\bold{b}) = \phi(\bold{a})+\phi(\bold{b}).
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