If A and B are both second-order tensors and t, u, v, and w are all...
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If A and B are both second-order tensors and t, u, v, and w are all vectors, prove the following identities using the indicial notation: (1) A:B=Tr( A·B' Tr(A·B") (2) (txu)·(v×w) = (t - v)(u · w)-(t·w)(u· v) (3) [t·(uxv)]w = (t w)(u× v)+ (u - w)(v×t)+(v · w)(t×u) If A and B are both second-order tensors and t, u, v, and w are all vectors, prove the following identities using the indicial notation: (1) A:B=Tr( A·B' Tr(A·B") (2) (txu)·(v×w) = (t - v)(u · w)-(t·w)(u· v) (3) [t·(uxv)]w = (t w)(u× v)+ (u - w)(v×t)+(v · w)(t×u)
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