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Unformatted text preview: shall This convenient practice will be followed write all indices as subscripts. throughout this book. 2.9. CONTRACTION We shall now consider some operations on tensors that generate new Let Aikl be a mixed tensor so that, in a transformation from the coor- tensors. dinates xa to za(a = 1,2,. . . ,n), we obtain _ . a2 ax0 ax7 a d A? (z) = - --- A" l k l ax* 833 a z k 831 P+(x) . If we equate the indices i and k and sum, we obtain the set of quantities...
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- Fall '05