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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.
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]
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.
Ricci calculus, and index notation more generally, distinguishes between lower indices (subscripts) and upper indices (superscripts); the latter are not exponents, even though they may look as such to the reader only familiar with other parts of mathematics.
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.
This framework came in 1975. [8] It emphasized that a curriculum based on the principles laid out in the framework has to be developed on the basis of research. Thus for NCERT, the 1970s was a decade flushed with curriculum research and development activities to narrate the content and process of education to Indian realities.
According to some authors, a principal submatrix is a submatrix in which the set of row indices that remain is the same as the set of column indices that remain. [ 18 ] [ 19 ] Other authors define a principal submatrix as one in which the first k rows and columns, for some number k , are the ones that remain; [ 20 ] this type of submatrix has ...
Full employment theorem (theoretical computer science) Fulton–Hansen connectedness theorem (algebraic geometry) Fundamental theorem of algebra (complex analysis) Fundamental theorem of arbitrage-free pricing (financial mathematics) Fundamental theorem of arithmetic (number theory) Fundamental theorem of calculus