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...

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

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...

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

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...

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

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...

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

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...

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...

\{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...

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...

the use of the musical notation symbols ♭ {\displaystyle \flat } (flat) and ♯ {\displaystyle \sharp } (sharp). In the notation of Ricci calculus and mathematical...

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

evaluated at x = a and D2 f (a) is the Hessian matrix. Applying the multi-index notation the Taylor series for several variables becomes T ( x ) = ∑ | α |...

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

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

such as hearing the shape of a drum and some proofs of the Atiyah–Singer index theorem. Infinite dimensional manifolds The definition of a manifold can...

{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...

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...

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

ones mixed. Notationally, these tensors differ from each other by the covariance/contravariance of their indices. A given contravariant index of a tensor...

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

sides by e ( a + b ) x . {\displaystyle e^{(a+b)x}.} : 69  With the multi-index notation for partial derivatives of functions of several variables, the Leibniz...