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It is common convention to use greek indices when writing expressions involving tensors in Minkowski space, while Latin indices are reserved for Euclidean space. Well-formulated expressions are constrained by the rules of Einstein summation : any index may appear at most twice and furthermore a raised index must contract with a lowered index.
The following are special examples of a homomorphism on a binary operation: Additive function: preserves the addition operation: f (x + y) = f (x) + f (y). Multiplicative function: preserves the multiplication operation: f (xy) = f (x)f (y). Relative to negation: Even function: is symmetric with respect to the Y-axis.
The entry of a matrix A is written using two indices, say i and j, with or without commas to separate the indices: a ij or a i,j, where the first subscript is the row number and the second is the column number. Juxtaposition is also used as notation for multiplication; this may be a source of confusion. For example, if
where i represents the index of summation; a i is an indexed variable representing each successive term in the series; m is the lower bound of summation, and n is the upper bound of summation. The term "i = m" under the summation symbol means that the index i starts equal to m. The index, i, is incremented by 1 for each successive term ...
In statistics and research design, an index is a composite statistic – a measure of changes in a representative group of individual data points, or in other words, a compound measure that aggregates multiple indicators. [1] [2] Indices – also known as indexes and composite indicators – summarize and rank specific observations. [2]
The index number problem is the term used by economists to describe the limitation of statistical indexing, when used as a measurement for cost-of-living increases. [7] For example, in the Consumer Price Index, a reference year's "market basket" is assigned an index number of 100.
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