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Math Help - Polytope

  1. #1
    Junior Member
    Joined
    Sep 2009
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    62

    Polytope

    Hi, I need help with this:
    Let P be a non-empty polytope.
    I) Prove that P has vertices.
    II)Let u_1, \dots u_l \in \mathbb{R}^n be the vectrices of P. Show that P=conv(\{u_1, \dots u_l \}).

    for the first one I see why P has vertices, if P is bounded and P=\{ x \colon Ax\leq b \} then if x \in P, x is also bounded so A must be full colon rank. But this is just an idea and I'm not even sure it's correct.

    if you can just give me a hit for II) it would be great.

    Thanks in advance!
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  2. #2
    MHF Contributor
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    Re: Polytope

    Hey sunmalus.

    For those who are not familiar with polytypes (like myself), what is the structure of a polytype (like the set structure)?
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