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Mathematical notation
Multi-index notation is a mathematical notation that simplifies formulas used in multivariable calculus, partial differential equations and the theory
Multi-index_notation
Tensor index notation for tensor-based calculations
In mathematics, Ricci calculus constitutes the rules of index notation and manipulation for tensors and tensor fields on a differentiable manifold, with
Ricci_calculus
Manner of referring to elements of arrays or tensors
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
Index_notation
Polynomial with only one term
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
Monomial
Expression that may be integrated over a region
dependent is zero. A common notation for the wedge product of elementary k {\displaystyle k} -forms is so called multi-index notation: in an n {\displaystyle
Differential_form
Mathematical notation for tensors and spinors
Abstract index notation (also referred to as slot-naming index notation) is a mathematical notation for tensors and spinors that uses indices to indicate
Abstract_index_notation
Mathematical Concept
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
Voigt_notation
Branch of mathematics
tensors Dyadic tensor Glossary of tensor theory Metric tensor Bra–ket notation Multilinear subspace learning Multivector Geometric algebra Clifford algebra
Multilinear_algebra
Shorthand notation for tensor operations
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
Einstein_notation
Notation of differential calculus
y\,\partial x}}.\end{aligned}}} So-called multi-index notation is used in situations when the above notation becomes cumbersome or insufficiently expressive
Notation_for_differentiation
Graphical notation for multilinear algebra calculations
In mathematics and physics, Penrose graphical notation or tensor diagram notation is a (usually handwritten) visual depiction of multilinear functions
Penrose_graphical_notation
Algebraic object with geometric applications
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
Tensor
Tensor equal to the negative of any of its transpositions
Antisymmetric permutation object acting on tensors Ricci calculus – Tensor index notation for tensor-based calculations Symmetric tensor – Tensor invariant under
Antisymmetric_tensor
Matrix operation which flips a matrix over its diagonal
another matrix, called the transpose of A and often denoted AT (among other notations). The transpose of a matrix was introduced in 1858 by the British mathematician
Transpose
Isomorphism between the tangent and cotangent bundles of a manifold
Einstein summation notation: any index may appear at most twice and furthermore a raised index must contract with a lowered index. With these rules we
Musical_isomorphism
Mathematical function of two variables; outputs 1 if they are equal, 0 otherwise
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
Kronecker_delta
Topological space that locally resembles Euclidean space
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
Manifold
Topics referred to by the same term
Multinomial distribution Multinomial logistic regression Multinomial test Multi-index notation Polynomial This disambiguation page lists mathematics articles associated
Multinomial
Origin and evolution of the symbols used to write equations and formulas
category theory by means of the concept of monoidal category. Later, multi-index notation eliminates conventional notions used in multivariable calculus, partial
History of mathematical notation
History_of_mathematical_notation
Algebraic operation on coordinate vectors
specified with respect to an orthonormal basis, is defined, in summation notation, as: a ⋅ b = ∑ i = 1 n a i b i = a 1 b 1 + a 2 b 2 + ⋯ + a n b n {\displaystyle
Dot_product
Mathematical approximation of a function
The last expression is the multivariate Taylor series in terms of multi-index notation with a full analogy to the single variable case. For example, for
Taylor_series
Tensor that describes the 4D geometry of spacetime
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
Metric tensor (general relativity)
Metric_tensor_(general_relativity)
Array of numbers
or no columns, called an empty matrix. The specifics of symbolic matrix notation vary widely, with some prevailing trends. Matrices are commonly written
Matrix_(mathematics)
Property of a mathematical space
phenomena Notation Abstract index notation Einstein notation Index notation Multi-index notation Penrose graphical notation Ricci calculus Tetrad (index notation)
Dimension
Operation in mathematics
2x2; often 3x3 or 4x4 are used, but any size is allowed. In simple index notation, this is written ∑ j = 1 2 a i j × b j k = c i k {\textstyle \sum
Tensor_contraction
denotes the partial derivative of order α {\displaystyle \alpha } (see multi-index notation). When σ = 1 {\displaystyle \sigma =1} , G σ ( Ω ) {\displaystyle
Gevrey_class
Method for specifying point positions
phenomena Notation Abstract index notation Einstein notation Index notation Multi-index notation Penrose graphical notation Ricci calculus Tetrad (index notation)
Coordinate_system
Data type that represents an ordered collection of elements (values or variables)
use to define such types and declare array variables, and special notation for indexing array elements. For example, in the Pascal programming language
Array_(data_type)
Straight path on a curved surface or a Riemannian manifold
phenomena Notation Abstract index notation Einstein notation Index notation Multi-index notation Penrose graphical notation Ricci calculus Tetrad (index notation)
Geodesic
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
Glossary_of_tensor_theory
Function space of all functions whose derivatives are rapidly decreasing
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
Schwartz_space
Branch of mathematics
popularised the tensor calculus of Ricci and Levi-Civita and introduced the notation g {\displaystyle g} for a Riemannian metric, and Γ {\displaystyle \Gamma
Differential_geometry
Mathematical object that describes the electromagnetic field in spacetime
}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:
Electromagnetic_tensor
Differential form of degree one or section of a cotangent bundle
phenomena Notation Abstract index notation Einstein notation Index notation Multi-index notation Penrose graphical notation Ricci calculus Tetrad (index notation)
One-form
Approximation of a function by a polynomial
{\partial f}{\partial x_{n}}}({\boldsymbol {a}})v_{n}.} Introduce the multi-index notation | α | = α 1 + ⋯ + α n , α ! = α 1 ! ⋯ α n ! , x α = x 1 α 1 ⋯ x n
Taylor's_theorem
Mathematical operation on vector spaces
differentiable, then a */ b is differentiable. However, these kinds of notation are not universally present in array languages. Other array languages may
Tensor_product
Exterior algebraic map taking tensors from p forms to n-p forms
}(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
Hodge_star_operator
Millennium Prize Problem
(see smooth function) such that, for every multi-index α {\displaystyle \alpha } (see multi-index notation) and any K > 0 {\displaystyle K>0} , there
Navier–Stokes existence and smoothness
Navier–Stokes_existence_and_smoothness
Conserved physical quantity; rotational analogue of linear momentum
_{z}\wedge \mathbf {e} _{x}\,,\end{aligned}}} or more compactly in index notation: L i j = x i p j − x j p i . {\displaystyle L_{ij}=x_{i}p_{j}-x_{j}p_{i}\
Angular_momentum
Theory of gravitation as curved spacetime
}} is the stress–energy tensor. All tensors are written in abstract index notation. Matching the theory's prediction to observational results for planetary
General_relativity
Generalization of the product rule in calculus
both sides by e ( a + b ) x . {\displaystyle e^{(a+b)x}.} With the multi-index notation for partial derivatives of functions of several variables, the Leibniz
General_Leibniz_rule
Algebraic expansion of powers of a binomial
{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
Binomial_theorem
Mathematical function, in linear algebra
Victor (2001) [1994], "Index theory", Encyclopedia of Mathematics, EMS Press: "The main question in index theory is to provide index formulas for classes
Linear_map
Notation used for Weyl spinors
indices, i.e. "index free notation", an overbar is retained on right-handed spinor, since ambiguity arises between chirality when no index is indicated
Van_der_Waerden_notation
Mapping from p forms to p-1 forms
phenomena Notation Abstract index notation Einstein notation Index notation Multi-index notation Penrose graphical notation Ricci calculus Tetrad (index notation)
Interior_product
Tensor having both covariant and contravariant indices
ones mixed. Notationally, these tensors differ from each other by the covariance/contravariance of their indices. A given contravariant index of a tensor
Mixed_tensor
Antisymmetric permutation object acting on tensors
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:
Levi-Civita_symbol
Type of differential equation
subscript u x i . {\displaystyle u_{x_{i}}.} For multiple derivatives, multi-index notation can be used. Thus if α = ( α 1 , … , α n ) {\displaystyle \alpha
Partial_differential_equation
Tensor in differential geometry
v 1 , … , v n {\displaystyle v_{1},\ldots ,v_{n}} . In abstract index notation, R i c a b = R c b c a = R c a c b . {\displaystyle \mathrm {Ric} _{ab}=\mathrm
Ricci_curvature
Set of vectors used to define coordinates
j}y_{j},} for i = 1, ..., n. This formula may be concisely written in matrix notation. Let A be the matrix of the a i , j {\displaystyle a_{i,j}} , and X = [
Basis_(linear_algebra)
Coordinate-free definition of a tensor
phenomena Notation Abstract index notation Einstein notation Index notation Multi-index notation Penrose graphical notation Ricci calculus Tetrad (index notation)
Tensor_(intrinsic_definition)
Covariant derivative of the metric tensor
, Y , Z {\displaystyle X,Y,Z} arbitrary vector fields. In abstract index notation, this reads Q a b c = ∇ a g b c {\displaystyle Q_{abc}=\nabla _{a}g_{bc}}
Nonmetricity_tensor
Tensor describing energy momentum density in spacetime
superscripted variables (not exponents; see Tensor index notation and Einstein summation notation). The four coordinates of an event of spacetime x are
Stress–energy_tensor
Affine connection on the tangent bundle of a manifold
phenomena Notation Abstract index notation Einstein notation Index notation Multi-index notation Penrose graphical notation Ricci calculus Tetrad (index notation)
Levi-Civita_connection
Scalar measure of the rotational inertia with respect to a fixed axis of rotation
\end{aligned}}} It is common in rigid body mechanics to use notation that explicitly identifies the x {\displaystyle x} , y {\displaystyle y}
Moment_of_inertia
Measure of the curvature of a pseudo-Riemannian manifold
v_{3}\right)k\left(v_{1},v_{4}\right)\end{aligned}}} In tensor component notation, this can be written as C i k ℓ m = R i k ℓ m + 1 n − 2 ( R i m g k ℓ −
Weyl_tensor
Form of musical notation for computers
ABC notation is a shorthand form of musical notation for computers. In basic form it uses the letter notation with a–g, A–G, and z, to represent the corresponding
ABC_notation
Format for notating atoms and molecules
Spectroscopic notation provides a way to specify atomic ionization states, atomic orbitals, and molecular orbitals. Spectroscopists customarily refer to
Spectroscopic_notation
Vector behavior under coordinate changes
covectors) are said to be contravariant. In Einstein notation (implicit summation over repeated index), contravariant components are denoted with upper indices
Covariance and contravariance of vectors
Covariance_and_contravariance_of_vectors
Operation on differential forms
of the space of one-forms, each associated with a coordinate. Given a multi-index I = ( i 1 , … , i k ) {\displaystyle I=(i_{1},\ldots ,i_{k})} with 1
Exterior_derivative
Continuous surjection satisfying a local triviality condition
phenomena Notation Abstract index notation Einstein notation Index notation Multi-index notation Penrose graphical notation Ricci calculus Tetrad (index notation)
Fiber_bundle
Infinite sum of monomials
product symbol, denoting multiplication. In the more convenient multi-index notation this can be written f ( x ) = ∑ α ∈ N n a α ( x − c ) α . {\displaystyle
Power_series
Mathematical function
ingredient of the proof is the following simple property, which uses multi-index notation for monomials in the variables Xi. Lemma. The leading term of eλt (X1
Elementary symmetric polynomial
Elementary_symmetric_polynomial
Specification of a derivative along a tangent vector of a manifold
coordinate-free language and using a local coordinate system and the traditional index notation. The covariant derivative of a tensor field is presented as an extension
Covariant_derivative
Theory of interwoven space and time by Albert Einstein
disconcerting to physicists of the time. Among other things, the presence of an index of refraction term meant that, since n {\displaystyle n} depends on wavelength
Special_relativity
Algebra associated to any vector space
given. Then any alternating tensor t ∈ Ar(V) ⊂ Tr(V) can be written in index notation with the Einstein summation convention as t = t i 1 i 2 ⋯ i r e i 1
Exterior_algebra
Function that is invariant under all permutations of its variables
phenomena Notation Abstract index notation Einstein notation Index notation Multi-index notation Penrose graphical notation Ricci calculus Tetrad (index notation)
Symmetric_function
phenomena Notation Abstract index notation Einstein notation Index notation Multi-index notation Penrose graphical notation Ricci calculus Tetrad (index notation)
Symmetrization
Tensor used in general relativity
a tensor of order 2 defined over pseudo-Riemannian manifolds. In index-free notation it is defined as G = R − 1 2 g R , {\displaystyle {\boldsymbol {G}}={\boldsymbol
Einstein_tensor
Assignment of a tensor continuously varying across a region of space
bundle – Construction in differential topology Ricci calculus – Tensor index notation for tensor-based calculations Spinor field – Geometric structurePages
Tensor_field
Structure defining distance on a manifold
is increased by du units, and v is increased by dv units. Using matrix notation, the first fundamental form becomes d s 2 = [ d u d v ] [ E F F G ] [ d
Metric_tensor
Musical symbols are marks and symbols in musical notation that indicate various aspects of how a piece of music is to be performed. There are symbols to
List_of_musical_symbols
Type of derivative in differential geometry
=f{\mathcal {L}}_{X}\omega +df\wedge i_{X}\omega .} In local coordinate notation, for a type ( r , s ) {\displaystyle (r,s)} tensor field T {\displaystyle
Lie_derivative
Tensor field in Riemannian geometry
the noncommutativity of the second covariant derivative. In abstract index notation, R d c a b Z c = ∇ a ∇ b Z d − ∇ b ∇ a Z d . {\displaystyle R^{d}{}_{cab}Z^{c}=\nabla
Riemann_curvature_tensor
Differential form
{\displaystyle \omega } is frequently used to denote the volume form, this notation is not universal; the symbol ω {\displaystyle \omega } often carries many
Volume_form
Second order tensor in vector algebra
algebra, a dyadic or dyadic tensor is a second order tensor, written in a notation that fits in with vector algebra. There are numerous ways to multiply two
Dyadics
Uniqueness for linear partial differential equations with real analytic coefficients
differential equations with real analytic coefficients. We will use the multi-index notation: Let α = { α 1 , … , α n } ∈ N 0 n , {\displaystyle \alpha =\{\alpha
Holmgren's_uniqueness_theorem
Decomposition in multilinear algebra
{\displaystyle M>2} and all I m ≥ 2 {\displaystyle I_{m}\geq 2} . For simplicity in notation, assume without loss of generality that the factors are ordered such that
Tensor_rank_decomposition
Spinning motion in theoretical physics
{\mathfrak {se}}(d)} . This article uses Cartesian coordinates and tensor index notation. The Noether current for translations in space is momentum, while the
Spin_tensor
Abbreviation in the fields of special and general relativity
four-dimensional spacetime. General four-tensors are usually written in tensor index notation as A ν 1 , ν 2 , . . . , ν m μ 1 , μ 2 , . . . , μ n {\displaystyle
Four-tensor
Branch of physics which studies the behavior of materials modeled as continuous media
phenomena Notation Abstract index notation Einstein notation Index notation Multi-index notation Penrose graphical notation Ricci calculus Tetrad (index notation)
Continuum_mechanics
Construct in differenital geometry
dx^{i}.} The point of the notation is to distinguish the indices j, k, which run over the n dimensions of the fiber, from the index i, which runs over the
Metric_connection
Non-tensorial representation of the spin group
form on a complex vector space is equivalent to the standard one, this notation is often used whenever dimℂ(V) = n. If n = 2k is even, then Cℓn(ℂ) is isomorphic
Spinor
Array of numbers describing a metric connection
the same notation as tensors with index notation, they do not transform like tensors under a change of coordinates. Contracting the upper index with either
Christoffel_symbols
Note: General relativity articles using tensors will use the abstract index notation. The principle of general covariance was one of the central principles
Mathematics of general relativity
Mathematics_of_general_relativity
Universal construction in multilinear algebra
was actually one and the same thing as ∇ {\displaystyle \nabla } ; and notational sloppiness here would lead to utter chaos. To strengthen this: the tensor
Tensor_algebra
is a rank-2 tensor defined over pseudo-Riemannian manifolds. In index-free notation it is defined as G = R − 1 2 g R , {\displaystyle \mathbf {G} =\mathbf
Introduction to the mathematics of general relativity
Introduction_to_the_mathematics_of_general_relativity
Geometric structure
phenomena Notation Abstract index notation Einstein notation Index notation Multi-index notation Penrose graphical notation Ricci calculus Tetrad (index notation)
Spinor_bundle
Representation of mechanical stress at every point within a deformed 3D object
_{1}+\sigma _{32}\mathbf {e} _{2}+\sigma _{33}\mathbf {e} _{3},} In index notation this is T ( e i ) = T j ( e i ) e j = σ i j e j . {\displaystyle \mathbf
Cauchy_stress_tensor
System of moving vectors in differential geometry
phenomena Notation Abstract index notation Einstein notation Index notation Multi-index notation Penrose graphical notation Ricci calculus Tetrad (index notation)
Parallel_transport
Ways of writing certain laws of physics
equations, one for each value of β. Using the antisymmetric tensor notation and comma notation for the partial derivative (see Ricci calculus), the second equation
Covariant formulation of classical electromagnetism
Covariant_formulation_of_classical_electromagnetism
Study of curves from a differential point of view
phenomena Notation Abstract index notation Einstein notation Index notation Multi-index notation Penrose graphical notation Ricci calculus Tetrad (index notation)
Differentiable_curve
Second-rank tensor in quantum chromodynamics
sum to be taken (e.g. "no sum"). Below the definitions (and most of the notation) follow K. Yagi, T. Hatsuda, Y. Miake and Greiner, Schäfer. The tensor
Gluon_field_strength_tensor
Tensor invariant under permutations of vectors it acts on
the operator is omitted: T1T2 = T1 ⊙ T2. In some cases an exponential notation is used: v ⊙ k = v ⊙ v ⊙ ⋯ ⊙ v ⏟ k times = v ⊗ v ⊗ ⋯ ⊗ v ⏟ k times =
Symmetric_tensor
Type of physical quantity
pseudotensor density according to the first definition. A change of variables in multi-dimensional integration may be achieved through the incorporation of a factor
Pseudotensor
Mathematics of smooth surfaces
Here hu and hv denote the two partial derivatives of h, with analogous notation for the second partial derivatives. The second fundamental form and all
Differential geometry of surfaces
Differential_geometry_of_surfaces
Construct allowing differentiation of tangent vector fields of manifolds
Y]=\left(X^{j}\partial _{j}Y^{i}-Y^{j}\partial _{j}X^{i}\right)\partial _{i}} in Einstein notation. This is independent of coordinate system choice and ∂ i = ( ∂ ∂ ξ i )
Affine_connection
Object in differential geometry
trace-free part and another part which contains the trace terms. Using the index notation, the trace of T is given by a i = T k i k , {\displaystyle a_{i}=T^{k}{}_{ik}
Torsion_tensor
Operation that pairs a left and a right R-module into an abelian group
_{R}N} . It is often called a pure tensor. Strictly speaking, the correct notation would be x ⊗R y but it is conventional to drop R here. Then, immediately
Tensor_product_of_modules
Electromagnetism in general relativity
square brackets indicate anti-symmetrization (see Ricci calculus for the notation). The covariant derivative of the electromagnetic field is F α β ; γ =
Maxwell's equations in curved spacetime
Maxwell's_equations_in_curved_spacetime
MULTI INDEX-NOTATION
MULTI INDEX-NOTATION
Girl/Female
Hindu, Indian
Index Finger
Boy/Male
Muslim
Expounder of Islamic Law.
Girl/Female
Hindu
Salvation, Freedom from life and death
Boy/Male
Hindu, Indian, Jain, Marathi
With Multi-coloured Body
Boy/Male
Bengali, Celebrity, Gujarati, Hindu, Indian, Kannada, Marathi, Punjabi, Sanskrit, Sikh, Sindhi, Traditional
The God of Weather and War; Lord of the Devas; King of Gods
Girl/Female
American, Australian, British, English
The Country India
Girl/Female
Indian, Punjabi, Sikh
Multi Talented
Boy/Male
Hindu
With multi-colored body
Boy/Male
Hindi
Supreme god.
Boy/Male
Hindu
Mukti, Emancipation, Liberation
Boy/Male
Hindu
An idol, All auspicious Lord, Lord Vishnu, Statue
Boy/Male
Muslim
Jurist
Boy/Male
Hindu, Indian, Marathi
Multi Talented Person; With Good Taste
Girl/Female
Welsh
Legendary daughter of GanKy.
Boy/Male
Tamil
Chirtrang | சிரà¯à®¤à¯à®°à®‚க
With multi-colored body
Chirtrang | சிரà¯à®¤à¯à®°à®‚க
Boy/Male
Tamil
Mukti, Emancipation, Liberation
Girl/Female
Hindu
A creeper with fragrant flowers
Girl/Female
Gujarati, Hindu, Indian, Jain, Kannada, Malayalam, Marathi, Oriya, Sanskrit, Sindhi, Tamil, Telugu
Freedom from Life and Death; Liberation; Valuable
Boy/Male
Sikh
Ruler of all that is wild and untamed., Born of tooth and fang
Boy/Male
Indian
Jurist
MULTI INDEX-NOTATION
MULTI INDEX-NOTATION
Surname or Lastname
English
English : variant spelling of Monk.
Boy/Male
Arabic, Muslim
Chief; Ruler; Traveller
Girl/Female
Greek
Of the universe.
Girl/Female
Muslim African Egyptian Arabic
Respected. Darling.
Male
Russian
(ДеÑÑ) Pet form of Russian Modest, DESYA means "moderate, sober."
Boy/Male
Muslim
Believer
Girl/Female
Tamil
Jyotishmati | ஜà¯à®¯à¯‹à®¤à®¿à®·à®®à®¤à®¿
Luminous, Lustrous
Boy/Male
Gujarati, Indian
Heaven
Male
English
Short form of English Alexander, ALIC means "defender of mankind."
Boy/Male
Indian, Punjabi, Sikh
One Absorbed in Naam
MULTI INDEX-NOTATION
MULTI INDEX-NOTATION
MULTI INDEX-NOTATION
MULTI INDEX-NOTATION
MULTI INDEX-NOTATION
pl.
of Index
n.
That which points out; that which shows, indicates, manifests, or discloses.
pl.
of Index
n.
The figure or letter which shows the power or root of a quantity; the exponent.
imp. & p. p.
of Index
adv.
In the manner of an index.
a.
Of, pertaining to, or like, an index; having the form of an index.
n.
The second digit, that next pollex, in the manus, or hand; the forefinger; index finger.
pl.
of Index
v. t.
To provide with an index or table of references; to put into an index; as, to index a book, or its contents.
p. pr. & vb. n.
of Index
n.
Index; indication.
n.
One who makes an index.
n.
A table for facilitating reference to topics, names, and the like, in a book; -- usually alphabetical in arrangement, and printed at the end of the volume.
n.
A prologue indicating what follows.
pl.
of Mufti
n.
That which guides, points out, informs, or directs; a pointer or a hand that directs to anything, as the hand of a watch, a movable finger on a gauge, scale, or other graduated instrument. In printing, a sign used to direct particular attention to a note or paragraph; -- called also fist.
n. pl.
See Index.