Dummy index, repeated

Dummy index repeated subscripts are called dummy subscripts, since they can be changed freely to another letter with no effect on the equation. 

The range convention and the summation convention will be used. The range convention is any subscript that appears only once on one side of an expression takes on values 1, 2, and 3. The summation convention is any subscript that appears twice on one side of an expression is summed from 1 to 3. The repeated index is called the dummy index. 

The repeated appearance of an index (j say) indicates that the lhs in an expression like x[ = aijXj (i = 1,2,3) is a sum over the dummy index j for all possible values (here j = 1,2,3). Whenever an index occurs two or more times in a term, it is implied, without any further symbols, that the terms are to be summed over all possible values of the index. 

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