Introduction to Tensor Analysis and the Calculus of Moving Surfaces by Pavel Grinfeld

Author:Pavel Grinfeld
Language: eng
Format: epub
Publisher: Springer New York, New York, NY

(9.10)

To show the equivalence of equations (9.9) and (9.10), note that switching the values 1 and 2 in the original definition results in the same value of opposite sign:

(9.11)

This observation can be applied to any pair of indices. In other words, the is skew-symmetric in r, s, and t. As we have previously learned, a third-order skew-symmetric system has a single degree of freedom, which can be identified as the entry corresponding to r,s,t = 1,2,3. By definition, for these values of the indices, is precisely A. This observation can be summarized as follows:

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