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Foundation Mathematics for the Physical Sciences by K. F. Riley, M. P. Hobson

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D

Summation convention

In the main text, particularly when dealing with matrices and vector calculus in three dimensions, we often need to take a sum over a number of terms which are all of the same general form, and differ only in the value of an indexing subscript or the symbol associated with each of the three different Cartesian coordinates. Thus the prescription for the elements of the product P of two matrices, A and B, might be written as

image

(D.1)

or the expression for the divergence of a vector a (see Chapter 11) given in the form

(D.2)

Sometimes, for example in a multiple matrix product, several sums appear in an expression, ...

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