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Essential Mathematical Methods for the Physical Sciences by K. F. Riley, M. P. Hobson

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E

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

image

(E.1)

follows. One further important property is that δii = 3, the trace of the unit matrix in three dimensions. ...

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