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Multilinear Maps of V^n into Reals and Effect of Linear Transforma

  1. Dec 28, 2013 #1

    WWGD

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    Hi, All:

    Is there a "nice" , non-messy way of showing this:

    Let [itex]M(v_1,v_2,..,v_n) → R+[/itex], where R is the Reals, be a multilinear map,

    where [itex] v_i[/itex] are vectors in a finite-dimensional vector space V.

    Now, let [itex] L: Vn → Vn [/itex] be a linear map with Det(L)>0 .

    How do we show that [itex]M(L(v_1,v_2,..,v_n))([/itex] is also strictly-positive? I think it

    has to see with the fact that the map L preserves the orientation of [itex]Vn[/itex],

    but I don't see how to make this more rigorous. Any ideas?
     
  2. jcsd
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