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  2. Raising and lowering indices - Wikipedia

    en.wikipedia.org/wiki/Raising_and_lowering_indices

    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.

  3. Multi-index notation - Wikipedia

    en.wikipedia.org/wiki/Multi-index_notation

    Multi-index notation is a mathematical notation that simplifies formulas used in multivariable calculus, partial differential equations and the theory of distributions, by generalising the concept of an integer index to an ordered tuple of indices.

  4. Index notation - Wikipedia

    en.wikipedia.org/wiki/Index_notation

    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]

  5. Symbolab - Wikipedia

    en.wikipedia.org/wiki/Symbolab

    Later, the ability to show all of the steps explaining the calculation were added. [6] The company's emphasis gradually drifted towards focusing on providing step-by-step solutions for mathematical problems at the secondary and post-secondary levels. Symbolab relies on machine learning algorithms for both the search and solution aspects of the ...

  6. Index calculus algorithm - Wikipedia

    en.wikipedia.org/wiki/Index_calculus_algorithm

    This was considered a minor step compared to the others for smaller discrete log computations. However, larger discrete logarithm records [ 1 ] [ 2 ] were made possible only by shifting the work away from the linear algebra and onto the sieve (i.e., increasing the number of equations while reducing the number of variables).

  7. Einstein notation - Wikipedia

    en.wikipedia.org/wiki/Einstein_notation

    In mathematics, especially the usage of linear algebra in mathematical physics and differential geometry, Einstein notation (also known as the Einstein summation convention or Einstein summation notation) is a notational convention that implies summation over a set of indexed terms in a formula, thus achieving brevity.