The Kronecker delta and Levi–Civita symbols
In a number of places in the main text and in Appendix D we have encountered and used the Kronecker delta, a two-subscript quantity δij defined by
As indicated in Appendix D, when used with the summation convention δij has the property aijδjk = aik for a general matrix A with elements aij. A particular case of this occurs when A is the unit matrix; then aij = δij and the result
follows. One further important property is that δii = 3, the trace of the unit matrix in three dimensions. ...