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601-index-notation

# 601-index-notation - MATH 601 AUTUMN 2008 The index...

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MATH 601, AUTUMN 2008 The index notation with the summing convention The index notation includes the following conventions: (a) In each term (“monomial”) forming a given expression, any index (that is, a subscript or superscript) may appear at most twice. (b) If an index appears once in one term, then it must appear once in every other term of the given expression, always in the same position (up or down). (c) If an index appears twice in one term, then it must appear once as a subscript and once as a superscript , and the term is to be summed over that index. In addition, ordered bases in an n -dimensional real or complex vector space V will often be written as e 1 , . . . , e n (or, briefly, just e j ), where n = dim V and the indices such as j, k, l are tacitly assumed to range from 1 to n . Another ordered basis of V then may be written as e 1 , . . . , e n (or, briefly, e j ), with the same core letter e and a different range of indices. The index sets { 1 , . . . , n } and { 1 , . . . , n } are just two disjoint sets of symbols representing numerals from 1 to n . Different vector spaces may be distinguished

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