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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: V^{n}→ V^{n}[/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]V^{n}[/itex],

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

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

Can you offer guidance or do you also need help?

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