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2. 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.

3. 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]

4. Schwartz space - Wikipedia

   en.wikipedia.org/wiki/Schwartz_space

   If is a multi-index, and a is a positive real number, then | | (). Any smooth function f with compact support is in 𝒮(R n).This is clear since any derivative of f is continuous and supported in the support of f, so has a maximum in R n by the extreme value theorem.

5. Raising and lowering indices - Wikipedia

   en.wikipedia.org/wiki/Raising_and_lowering_indices

   Concretely, in the case where the vector space has an inner product, in matrix notation these can be thought of as row vectors, which give a number when applied to column vectors. We denote this by V ∗ := Hom ( V , K ) {\displaystyle V^{*}:={\text{Hom}}(V,K)} , so that α ∈ V ∗ {\displaystyle \alpha \in V^{*}} is a linear map α : V → K ...

6. Glossary of tensor theory - Wikipedia

   en.wikipedia.org/wiki/Glossary_of_tensor_theory

   The earliest foundation of tensor theory – tensor index notation. [1] Order of a tensor The components of a tensor with respect to a basis is an indexed array. The order of a tensor is the number of indices needed. Some texts may refer to the tensor order using the term degree or rank. Rank of a tensor

7. Glossary of mathematical symbols - Wikipedia

   en.wikipedia.org/wiki/Glossary_of_mathematical...

   This notation has also been used for other variants of floor and ceiling functions. 4. Iverson bracket: if P is a predicate, [] may denote the Iverson bracket, that is the function that takes the value 1 for the values of the free variables in P for which P is true, and takes the value 0 otherwise.