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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.
Each index has one possible value per dimension of the underlying vector space. The number of indices equals the degree (or order) of the tensor. For compactness and convenience, the Ricci calculus incorporates Einstein notation, which implies summation over indices repeated within a term and universal quantification over free indices ...
A punched card (also punch card [1] or punched-card [2]) is a piece of card stock that stores digital data using punched holes. Punched cards were once common in data processing and the control of automated machines .
A computer punched card reader or just computer card reader is a computer input device used to read computer programs in either source or executable form and data from punched cards. A computer card punch is a computer output device that punches holes in cards. Sometimes computer punch card readers were combined with computer card punches and ...
A notched card showing two levels of notching. Edge-notched cards or edge-punched cards are a system used to store a small amount of binary or logical data on paper index cards, encoded via the presence or absence of notches in the edges of the cards. [1]
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A vector treated as an array of numbers by writing as a row vector or column vector (whichever is used depends on convenience or context): = (), = Index notation allows indication of the elements of the array by simply writing a i, where the index i is known to run from 1 to n, because of n-dimensions. [1]
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