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Inner Product Spaces
For a fixed vector w ∈ V, one may define the map T: V → F as Tv= v,w.Thismap is linear by condition 1 of Definition 1. This implies in particular that 0,w =0forevery w ∈ V. By the conjugate symmetry we also have w,0 =0. Lemma 2. The inner product is anti-linear in the second slot, that is, u,v+w = u,v + u,w for all u,v,w ∈ V and u,av ...
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LECTURE 5 - UC Davis Mathematics
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