Given a non-zero vector 𝐯, find the value that should be assigned to αto make Pi j=αvi vj and Qi j=δi j-αvi vj into parallel and orthogonal projection tensors, respectively, i.e. tensors that satisfy, respectively, Pi j vj=vi, Pi j uj=0 and Qi j vj=0, Qi j uj=ui, for any vector u that is orthogonal to 𝐯. Show, in particular, that Qi j is unique, i.e. that if another tensor Ti j has the same properties as Qi j then (Qi j-Ti j) wj=0 for any vector 𝐰. | Numerade
Given a non-zero vector 𝐯, find the value that should be assigned to α…
Oct 13, 2021
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