Ex.6. If Aj is a covariant tensor of the second order and Bi, C' are contravariant vectors; prove that ABİC' is an invariant.
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- For the following line elements and vector V μ, write down the metric, the inverse metric, and find rest on pictureDescribe all vectors in span{(3,0,2), (-2,0,3)} (so computationally what do the vectors look like?). Also give a geometric description for these vectors (what space are you in and visually what do you get? Be as descriptive as you can!).42 Let Ta denote the translation operator (displacement vector d); let D(n,p) denote the rotation operator ( and are the axis and angle of rotation, respectively); and let denote the parity operator. Which, if any, of the following pairs commute? Why? (a) Ta and T (d and d' in different directions). (b) D(n,p) and D(n, ') (ñ and f' in different directions). (c) T₁ and . (d) D(n,) and .