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Thread: Exactly two subspaces

  1. #1

    Exactly two subspaces

    Suppose that V is a vector space. How can I prove that dimV=1 if and only if V has exactly two subspaces?

  2. #2
    Elite Member
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    Quote Originally Posted by Georgegr View Post
    Suppose that V is a vector space. How can I prove that dimV=1 if and only if V has exactly two subspaces?
    Please post what you understand about this question.
    For example: What are the two subspaces (some call them trivial) of any v-space?
    If [tex]v\in V~\&~v\ne 0[/tex] does [tex]span\{v\}=V~?[/tex]
    “A professor is someone who talks in someone else’s sleep”
    W.H. Auden

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