Multi-index notation is a mathematical notation that simplifies formulas used in multivariable calculus, partial differential equations and the theory...

In mathematics, Ricci calculus constitutes the rules of index notation and manipulation for tensors and tensor fields on a differentiable manifold, with...

In mathematics and computer programming, index notation is used to specify the elements of an array of numbers. The formalism of how indices are used varies...

substituting by 1 the extra variable. The multi-index notation is often useful for having a compact notation, specially when there are more than two or...

Abstract index notation (also referred to as slot-naming index notation) is a mathematical notation for tensors and spinors that uses indices to indicate...

implies summation over a set of indexed terms in a formula, thus achieving brevity. As part of mathematics it is a notational subset of Ricci calculus; however...

linearly dependent is zero. A common notation for the wedge product of elementary k-forms is so called multi-index notation: in an n-dimensional context, for...

associated names for this idea: Mandel notation, Mandel–Voigt notation and Nye notation are others found. Kelvin notation is a revival by Helbig of old ideas...

of tensor theory – tensor index notation. Order of a tensor The components of a tensor with respect to a basis is an indexed array. The order of a tensor...

general contraction operation is sometimes called the trace. In tensor index notation, the basic contraction of a vector and a dual vector is denoted by f...

tensors Dyadic tensor Glossary of tensor theory Metric tensor Bra–ket notation Multilinear subspace learning Multivector Geometric algebra Clifford algebra...

matrix A by producing another matrix, often denoted by AT (among other notations). The transpose of a matrix was introduced in 1858 by the British mathematician...

or no columns, called an empty matrix. The specifics of symbolic matrix notation vary widely, with some prevailing trends. Matrices are commonly written...

In mathematics and physics, Penrose graphical notation or tensor diagram notation is a (usually handwritten) visual depiction of multilinear functions...

Multinomial distribution Multinomial logistic regression Multinomial test Multi-index notation Polynomial This disambiguation page lists mathematics articles associated...

Antisymmetric permutation object acting on tensors Ricci calculus – Tensor index notation for tensor-based calculations Symmetric tensor – Tensor invariant under...

calculus. Tensor notation makes use of upper and lower indexes on objects that are used to label a variable object as covariant (lower index), contravariant...

y\,\partial x}}.\end{aligned}}} So-called multi-index notation is used in situations when the above notation becomes cumbersome or insufficiently expressive...

abstract index notation is a way to write tensors such that the indices are no longer thought of as numerical, but rather are indeterminates. This notation captures...

g_{\rho \sigma }.} The metric tensor plays a key role in index manipulation. In index notation, the coefficients g μ ν {\displaystyle g_{\mu \nu }} of...

displaying wikidata descriptions as a fallback Ricci calculus – Tensor index notation for tensor-based calculations Spinor field – Geometric structurePages...

\{k\in \mathbb {N} :1\leq k\leq n\}} , and u i {\displaystyle u_{i}} is a notation for the image of i {\displaystyle i} by the function/vector u {\displaystyle...

multiplication as a sum of outer products. The generalized Kronecker delta or multi-index Kronecker delta of order 2 p {\displaystyle 2p} is a type ( p , p ) {\displaystyle...

}F_{\beta \gamma }+\partial _{\beta }F_{\gamma \alpha }=0} or using the index notation with square brackets[note 1] for the antisymmetric part of the tensor:...

lower case epsilon ε or ϵ, or less commonly the Latin lower case e. Index notation allows one to display permutations in a way compatible with tensor analysis:...

{d}}y_{d}^{n_{d}-k_{d}}.} This may be written more concisely, by multi-index notation, as ( x + y ) α = ∑ ν ≤ α ( α ν ) x ν y α − ν . {\displaystyle (x+y)^{\alpha...

for example we cannot lower the index of a ( 0 , 2 ) {\displaystyle (0,2)} tensor.) Ricci calculus Einstein notation Metric tensor Musical isomorphism...

(dy\wedge dz)&=dt\wedge dx\,.\end{aligned}}} These are summarized in the index notation as ⋆ ( d x μ ) = η μ λ ε λ ν ρ σ 1 3 ! d x ν ∧ d x ρ ∧ d x σ , ⋆ ( d...

Here, sup {\displaystyle \sup } denotes the supremum, and we used multi-index notation, i.e. x α := x 1 α 1 x 2 α 2 … x n α n {\displaystyle {\boldsymbol...

Scope Notation Abstract index notation Einstein notation Index notation Multi-index notation Penrose graphical notation Ricci calculus Tetrad (index notation)...