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3. Show that (1.6b) can be expressed in the form (1.8). What is the tensor A? (Notice that a general 4-tensor on two-dimensional space is
3. Show that (1.6b) can be expressed in the form (1.8). What is the tensor A? (Notice that a general 4-tensor on two-dimensional space is determined by the 24 = 16 entries Aijk However, the symmetry conditions (1.9) imply that such an A has only six independent entries, namely, Alm. Am2 = A1121 = A1211 = A2111, A1122 = A2211, A1212 = A1221 = A2112 = A2121, A 1222 = A2212 = A2221 = A2122, A2222.) = 2a ++ tr(), (1.6b) o = AE, (1.8) that is, 2 2 0jj = AijkEh, i, j = 1, 2. kul II 3. Show that (1.6b) can be expressed in the form (1.8). What is the tensor A? (Notice that a general 4-tensor on two-dimensional space is determined by the 24 = 16 entries Aijk However, the symmetry conditions (1.9) imply that such an A has only six independent entries, namely, Alm. Am2 = A1121 = A1211 = A2111, A1122 = A2211, A1212 = A1221 = A2112 = A2121, A 1222 = A2212 = A2221 = A2122, A2222.) = 2a ++ tr(), (1.6b) o = AE, (1.8) that is, 2 2 0jj = AijkEh, i, j = 1, 2. kul
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