Solution: Using the properties of the permutation symbol for the shift of the subindex and the e−δ identity given in Eq. (2.14), we obtain (2.38c)eijkejki=eijkeijk=δjjδkk−δjkδkj=δjjδkk−δjj=3×3−3=6. 4. eijkAjAk=0 Solution: This problem involves the cross-multi...
The Kronecker symbol δji has corresponding matrix elements given by the 3 × 3 identity matrix I. It may be interpreted as a second-order mixed tensor, where whichever of the covariant or contravariant components occurs first is immaterial, since if we substitute T = I in either of the tra...
The Levi-Civita symbol is a mathematical symbol used to represent the sign of a permutation. It takes the value of +1 if the permutation is even and -1 if the permutation is odd. The Kronecker delta is a mathematical symbol used to represent the identity matrix in linear algebra. ...