Unformatted text preview: U is free on v , v , we may deﬁne f , f : U → F by f ( v ) = f ( v ) = 1 and f ( v ) = f ( v ) = 0. We may extend f , f to the whole of V by deﬁning f ( w ) = f ( w ) = 0 for all w ∈ W . Then f ⊗ f ( v ⊗ v ) = 1 and f ( v ⊗ v ) = 0. Applying f ⊗ f to v ⊗ v = v ⊗ v , we deduce that 1 = 0 which is a contradiction and the result is proven....
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 Fall '07
 PALinnell
 Linear Algebra, Algebra, Vector Space, dimensional vector spaces

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