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Mathematical notation
A "hat" (circumflex (ˆ)), placed over a symbol is a mathematical notation with various uses. In statistics, a circumflex (ˆ), nicknamed a "hat", is used
Hat_notation
Notation for quantum states
Bra–ket notation or Dirac notation is a mathematical notation for linear algebra and linear operators on complex vector spaces together with their dual
Bra–ket_notation
Musical notation for percussive instruments
Percussion notation is a type of musical notation indicating notes to be played by percussion instruments. As with other forms of musical notation, sounds
Percussion_notation
Mathematics notation where operators follow operands
Polish notation (RPN), also known as reverse Łukasiewicz notation, Polish postfix notation or simply postfix notation, is a mathematical notation in which
Reverse_Polish_notation
Latin letter X with circumflex
it can also represent the predicted value for x, consistent with the hat notation. Bergsland, Knut (1994). Aleut Dictionary = Unangam Tunudgusii: an unabridged
X̂
Use of coordinates for representing vectors
Vector notation In mathematics and physics, vector notation is a commonly used notation for representing vectors, which may be Euclidean vectors, or more
Vector_notation
Type of heuristic technique
: T ) , {\displaystyle P(a_{T+1}|{\hat {a}}_{1:T},o_{1:T}),} where the "hat"-notation a ^ t {\displaystyle {\hat {a}}_{t}} denotes the fact that a t
Thompson_sampling
System of symbolic representation
Mathematical notation consists of using symbols for representing operations, unspecified numbers, relations, and any other mathematical objects and assembling
Mathematical_notation
Windows Runtime extension for C++ compilers
activated, using ref new and assigned to variables declared with the ^ (hat) notation inherited from C++/CLI. Foo^ foo = ref new Foo(); A WinRT variable is
C++/CX
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
Percussion instrument
A hi-hat, hihat, or high-hat is a combination of two cymbals and a pedal, all mounted on a metal stand. It is a part of the standard drum kit used by
Hi-hat
Windows Runtime library for C++
non-standard extensions to the C++ language, such as the ref new and ^ (hat) notation inherited from C++/CLI. It hadn't been fully appreciated then that advances
C++/WinRT
Typographical mark (^)
CARET U+2227 ∧ LOGICAL AND U+FF3E ＾ FULLWIDTH CIRCUMFLEX ACCENT Hat operator, a notation used in mathematics and statistics, is sometimes called a caret
Caret
Vector of length one
Cartesian coordinate system. The notations (î, ĵ, k̂), (x̂1, x̂2, x̂3), (êx, êy, êz), or (ê1, ê2, ê3), with or without hat, are also used, particularly in
Unit_vector
Mathematical model of the time dependence of a point in space
ems-with-multidimensional-complex-and-other-exotic-kinds-of-time The hat notation here is introduced to stress the fact that the map is a general operator
Dynamical_system
Setting of relativistic physics in geometric algebra
i {\displaystyle {\hat {\sigma }}_{i}} are the Pauli matrices (with the 'hat' notation indicating that σ ^ {\displaystyle {\hat {\sigma }}} is a
Spacetime_algebra
Popular Mexican dance
(2015). "The Basic Steps in the Jarabe Tapatío (Mexican Hat Dance): A Review Through Its Notation" (PDF). International Council of Kinetography Laban. Proceedings
Mexican_hat_dance
Type of permutation of a set of elements
subfactorial of n or n th de Montmort number (after Pierre Remond de Montmort). Notations for subfactorials in common use include Dn, dn, !n, or n¡ . For n > 0
Derangement
Emphasis on a note
about articulation on page 156 in his book Music Notation: Theory and Technique for Music Notation, where marcato accent in the third mark shown is referred
Accent_(music)
This is a list of common physical constants and variables, and their notations. Note that bold text indicates that the quantity is a vector. List of letters
List of common physics notations
List_of_common_physics_notations
Circulation density in a vector field
to the line integral of the vector field around the boundary curve. The notation curl F is more common in English-speaking countries. In the rest of the
Curl_(mathematics)
Quantum operator for the sum of energies of a system
quantum physics. Similar to vector notation, it is typically denoted by H ^ {\displaystyle {\hat {H}}} , where the hat indicates that it is an operator
Hamiltonian (quantum mechanics)
Hamiltonian_(quantum_mechanics)
Numbers in the Roman numeral system
symbol precedes a larger one, subtraction is implied; for example, the notation IV represents 5 − 1 = 4 and IX represents 10 − 1 = 9. The use of Roman
Roman_numerals
Simplified percussion notation
first presented in standard notation; following is the corresponding pattern translated into drum tab. B = Bass drum HH = Hi-hat S = Snare drum HH|x-x-x-x-x-x-x-x-||
Drum_tablature
\alpha |=(|\alpha \rangle )^{\dagger }} . See "bra–ket notation". Bra–ket notation The bra–ket notation is a way to represent the states and operators of a
Glossary of elementary quantum mechanics
Glossary_of_elementary_quantum_mechanics
Language of mathematics Mathematical notation Notation in probability and statistics Physical constants Notational systems in geometry: Christoffel symbols
Glossary of mathematical symbols
Glossary_of_mathematical_symbols
have some commonly used conventions, in addition to standard mathematical notation and mathematical symbols. Random variables are usually written in upper
Notation in probability and statistics
Notation_in_probability_and_statistics
Notation used for Weyl spinors
2 , 1 ˙ , 2 ˙ {\displaystyle {\hat {\alpha }}=(\alpha ,{\dot {\alpha }})=1,2,{\dot {1}},{\dot {2}}} In this notation the Dirac adjoint (also called the
Van_der_Waerden_notation
Tensor index notation for tensor-based calculations
Waerden notation for spinors, which uses hats and overdots on indices to reflect the chirality of a spinor. Ricci calculus, and index notation more generally
Ricci_calculus
ESPNcricinfo. "Most wickets For Women's Big Bash League". ESPNcricinfo. "WBBL Hat-tricks". ESPNcricinfo. "Best economy rates For Women's Big Bash League".
List of Women's Big Bash League records and statistics
List_of_Women's_Big_Bash_League_records_and_statistics
Origin and evolution of the symbols used to write equations and formulas
mathematical notation covers the introduction, development, and cultural diffusion of mathematical symbols and the conflicts between notational methods that
History of mathematical notation
History_of_mathematical_notation
Topics referred to by the same term
hatchback 10/6 may refer to: October 6 (month-day date notation) June 10 (day-month date notation) 10 shillings and 6 pence in UK pre-decimal currency The
106
Topics referred to by the same term
in statistics Hat operator, notation used in mathematics Hat function, alternate name for the triangular function The hat tile, a solution to the einstein
Hat_(disambiguation)
Algebraic object with geometric applications
pairs of indices may be summed this way. Penrose graphical notation is a diagrammatic notation which replaces the symbols for tensors with shapes, and their
Tensor
Mathematical gradient operator in certain coordinate systems
common curvilinear coordinate systems. This article uses the standard notation ISO 80000-2, which supersedes ISO 31-11, for spherical coordinates (other
Del in cylindrical and spherical coordinates
Del_in_cylindrical_and_spherical_coordinates
Concept in linear algebra
=\mathbf {a} -\operatorname {proj} _{\mathbf {b} }\mathbf {a} .} To simplify notation, this article defines a 1 := proj b a {\displaystyle \mathbf {a} _{1}:=\operatorname
Vector_projection
A hat-trick in cricket is when a bowler takes three wickets from consecutive deliveries. It is a relatively rare feat in women's international cricket
List of women's international cricket hat-tricks
List_of_women's_international_cricket_hat-tricks
Specialized notation for multivariable calculus
In mathematics, matrix calculus is a specialized notation for doing multivariable calculus, especially over spaces of matrices. It collects the various
Matrix_calculus
Data interface description language
Abstract Syntax Notation One (ASN.1) is a standard interface description language (IDL) for defining data structures that can be serialized and deserialized
ASN.1
Derivative of a function with respect to time
{\displaystyle t} . A variety of notations are used to denote the time derivative. In addition to the normal (Leibniz's) notation, d x d t {\displaystyle {\frac
Time_derivative
Music notation software
Studio (branded as MuseScore before 2024) is a free and open-source music notation program for Windows, macOS, and Linux under the Muse Group, which owns
MuseScore
Scalar measure of the rotational inertia with respect to a fixed axis of rotation
{\hat {k}} \times \Delta r_{i}\mathbf {\hat {e}} _{i}-\omega \mathbf {\hat {k}} \times \omega \mathbf {\hat {k}} \times \Delta r_{i}\mathbf {\hat {e}}
Moment_of_inertia
This is a list of the notation used in Alfred North Whitehead and Bertrand Russell's Principia Mathematica (1910–1913). The second (but not the first)
Glossary of Principia Mathematica
Glossary_of_Principia_Mathematica
Fact that observing a situation changes it
Classical mechanics Old quantum theory Interference Fundamentals Bra–ket notation Complementarity Energy level Entanglement Hamiltonian Measurement Nonlocality
Observer_effect_(physics)
Theorem in statistics and econometrics
y_{i}={\hat {\beta }}_{0}+{\hat {\beta }}_{1}x_{1i}+{\hat {\beta }}_{2}x_{2i}+\cdots +{\hat {\beta }}_{k}x_{ki}+{\hat {e}}_{i}} , where the hats denote
Frisch–Waugh–Lovell_theorem
Description of a quantum-mechanical system
representations of wave functions; in Dirac notation, they are written ρ ^ = | Ψ ⟩ ⟨ Ψ | . {\displaystyle {\hat {\rho }}=|\Psi \rangle \langle \Psi |.} The
Schrödinger_equation
Theorem about the dual of a Hilbert space
\left\langle \cdot \,,\cdot \right\rangle _{H}} while in physics, the bra–ket notation ⟨ ⋅ ∣ ⋅ ⟩ {\displaystyle \left\langle \cdot \mid \cdot \right\rangle }
Riesz_representation_theorem
Vector operator in vector calculus
{F} \cdot \mathbf {\hat {n}} \,dS} where |V| is the volume of V, S(V) is the boundary of V, and n ^ {\displaystyle \mathbf {\hat {n}} } is the outward
Divergence
Statistical error measure
− y ^ | {\displaystyle \mathbb {E} |y-{\hat {y}}|} is f ^ ( x ) = Median ( y | X = x ) {\displaystyle {\hat {f}}(x)={\text{Median}}(y|X=x)} . Proof:
Mean_absolute_error
Statistical method
}}} . Often these n equations are stacked together and written in matrix notation as y = X β + ε , {\displaystyle \mathbf {y} =\mathbf {X} {\boldsymbol {\beta
Multiple_linear_regression
Matrices important in quantum mechanics and the study of spin
{\displaystyle {\boldsymbol {\hat {x}}}_{2}} , and x ^ 3 {\displaystyle {\boldsymbol {\hat {x}}}_{3}} are an equivalent notation for the more familiar x ^
Pauli_matrices
Calculation rule in quantum mechanics
normalized wave function | ψ ⟩ {\displaystyle |\psi \rangle } (see Bra–ket notation), corresponds to a self-adjoint operator A {\displaystyle A} whose spectrum
Born_rule
Pictorial computational technique in quantum chemistry
states in bra–ket notation and include the abstract nature of the state, such as tensor products and transformation rules. The notation parallels the idea
Angular momentum diagrams (quantum mechanics)
Angular_momentum_diagrams_(quantum_mechanics)
Mathematical operation on vectors in 3D space
mathematics, the wedge notation a ∧ b is often used (in conjunction with the name vector product), although in pure mathematics such notation is usually reserved
Cross_product
Theorem in quantum mechanics
′ ( x ^ ) . {\displaystyle im[{\hat {H}},{\hat {x}}]=\hbar {\hat {p}},\qquad i[{\hat {H}},{\hat {p}}]=-\hbar V'({\hat {x}}).} Assuming that observables
Ehrenfest_theorem
Loss of quantum coherence
{\displaystyle {\hat {H}}={\hat {H}}_{S}\otimes {\hat {I}}_{B}+{\hat {I}}_{S}\otimes {\hat {H}}_{B}+{\hat {H}}_{I},} where H ^ S , H ^ B {\displaystyle {\hat {H}}_{S}
Quantum_decoherence
Statistical confidence interval for success counts
~{\hat {p}}\pm {\frac {z_{\alpha }}{\sqrt {n\ }}}{\sqrt {{\hat {p}}\left(1-{\hat {p}}\right)\ }}\ ,} where p ^ ≡ n s n {\displaystyle \ {\hat {p}}\equiv
Binomial proportion confidence interval
Binomial_proportion_confidence_interval
Notation in quantum physics
optionally in order to specify a level. L is written using spectroscopic notation: for example, it is written "S", "P", "D", or "F" to represent L = 0, 1
Term_symbol
Cylindrical drum
Standard drum notation for (up to six) toms.play
Tom_drum
hat-trick". Wide World of Sports. Retrieved 28 December 2025. Cameron, Louis (9 January 2020). "Unlikely batting hero saves Sixers after Rashid hat-trick"
List of Big Bash League records and statistics
List_of_Big_Bash_League_records_and_statistics
Mathematical entity to describe the probability of each possible measurement on a system
general have quantum uncertainty for the given observable. Using bra–ket notation, this linear combination of eigenstates can be represented as: | Ψ ( t
Quantum_state
Ternary operation on vectors
}{\hat {c}}_{\nu }={\hat {a}}_{\beta }{\hat {b}}_{\alpha }{\hat {c}}_{\beta }-{\hat {a}}_{\beta }{\hat {b}}_{\beta }{\hat {c}}_{\alpha }\\&=\left({\hat {b}}_{\alpha
Triple_product
Musical instrument consisting of a collection of percussion instruments
the drums and cymbals, as well as pedals to operate the bass drum and hi-hat, allowing them to adapt the sound to their desired effect. The drum set is
Drum_kit
Percussion using voice
snare drum, and /ts/ ([t͡s]) is usually the hi-hat (in 4 4: 𝄆b-ts-k-ts-b-ts-k-ts𝄇). Standard Beatbox Notation (SBN) was created by Mark Splinter and Gavin
Beatboxing
Function acting on the space of physical states in physics
relative to the orthonormal eigenbasis of A ^ {\displaystyle {\hat {A}}} ). In bra–ket notation the above can be written; A ^ ψ = A ^ ψ ( r ) = A ^ ⟨ r ∣ ψ
Operator_(physics)
Statistical measure
\operatorname {RMSD} ({\hat {\theta }})={\sqrt {\operatorname {MSE} ({\hat {\theta }})}}={\sqrt {\operatorname {E} {\big (}({\hat {\theta }}-\theta )^{2}{\big
Root_mean_square_deviation
Vector field representation in 3D curvilinear coordinate systems
systems arising in the natural world. Note: This page uses common physics notation for spherical coordinates, in which θ {\displaystyle \theta } is the angle
Vector fields in cylindrical and spherical coordinates
Vector_fields_in_cylindrical_and_spherical_coordinates
notation (100) indicates that a batsman scored 100 runs and was out (100*) indicates that a batsman scored 100 runs and was not out Bowling notation (5/20)
List of Women's Premier League (cricket) records and statistics
List_of_Women's_Premier_League_(cricket)_records_and_statistics
Statistical test
P ) → n → ∞ D χ Q 2 / Q , {\displaystyle (R{\hat {\theta }}_{n}-r)'[R({\hat {V}}_{n}/n)R']^{-1}(R{\hat {\theta }}_{n}-r)/Q\quad \xrightarrow {\mathcal
Wald_test
Circus skill manipulating objects
spinning, devil sticks, poi, cigar boxes, contact juggling, hooping, yo-yo, hat manipulation and kick-ups. The words juggling and juggler derive from the
Juggling
Volume of fluid which passes per unit time
the notation q v {\displaystyle q_{v}} and q m {\displaystyle q_{m}} for volumetric flow and mass flow respectively, to distinguish from the notation Q
Volumetric_flow_rate
Quantum physics concept
A ^ ≠ 0 ^ . {\displaystyle \left[{\hat {A}},{\hat {B}}\right]:={\hat {A}}{\hat {B}}-{\hat {B}}{\hat {A}}\neq {\hat {0}}.} Incompatible observables cannot
Complementarity_(physics)
Technology for controlling access to file system items
this. Permissions are commonly represented in symbolic or octal notation. Symbolic notation is used in the long output format of command ls -l. The first
File-system_permissions
Probability distribution
{4\left({\hat {\beta }}-{\hat {\alpha }}\right)^{2}\left(1+{\hat {\alpha }}+{\hat {\beta }}\right)}{{\hat {\alpha }}{\hat {\beta }}\left(2+{\hat {\alpha
Beta_distribution
Diacritical mark (◌̂)
sometimes used for an angle. For instance, the angles  or ABC^. In vector notation, a hat above a letter indicates a unit vector (a dimensionless vector with
Circumflex
Branch of physics describing the motion of objects without considering forces
^{2}{\hat {\mathbf {\theta } }}.} Using this notation, r(t) takes the form, r ( t ) = r r ^ + z ( t ) z ^ . {\displaystyle \mathbf {r} (t)=r{\hat {\mathbf
Kinematics
Number of values in the final calculation of a statistic that are free to vary
Z_{n}} . The restriction to three groups and equal sample sizes simplifies notation, but the ideas are easily generalized. The observations can be decomposed
Degrees of freedom (statistics)
Degrees_of_freedom_(statistics)
Measure of the error of an estimator
\left(Y_{i}-{\hat {Y_{i}}}\right)^{2}} . This is an easily computable quantity for a particular sample (and hence is sample-dependent). In matrix notation, MSE
Mean_squared_error
Sequence of characters that forms a search pattern
Stephen Cole Kleene described regular languages using his mathematical notation called regular events. These arose in theoretical computer science, in
Regular_expression
Theorem in quantum mechanics
zero. Using Dirac's bra–ket notation these two conditions are written as H ^ λ | ψ λ ⟩ = E λ | ψ λ ⟩ , {\displaystyle {\hat {H}}_{\lambda }|\psi _{\lambda
Hellmann–Feynman_theorem
Electromagnetic stress
Maxwell) is the stress tensor of an electromagnetic field. In tensor index notation it is given by: σ i j = ε 0 E i E j + 1 μ 0 B i B j − ( ε 0 2 E 2 + B 2
Maxwell_stress_tensor
Regularization method for artificial neural networks
x_{j}} – input from node j {\displaystyle j} This can be written in vector notation as y {\displaystyle \mathbf {y} } – output vector W {\displaystyle \mathbf
Dropout_(neural_networks)
Fantasy/mystery book series by Jim Butcher
2008. Whiteside, Lee (2007). "A Conversation With Jim Butcher" (PDF). ConNotations. 17 (2). Archived from the original (PDF) on March 20, 2012. Retrieved
The_Dresden_Files
Equation in statistical mechanics
( k ) , {\displaystyle {\hat {h}}(\mathbf {k} )\;=\;{\hat {c}}(\mathbf {k} )\;+\;\rho \;{\hat {h}}(\mathbf {k} )\;{\hat {c}}(\mathbf {k} )~,} which
Ornstein–Zernike_equation
Device attached to musical instrument to change its sound
particular can easily play softly without additional equipment. Musical notation directing players to mute and unmute their instruments varies. The type
Mute_(music)
Mathematical function often applied to matrices
nor implies Lipschitz continuity. For clarity and generality, the modern notation defines a greatest lower bound (or simply lower) logarithmic norm m [ A
Logarithmic_norm
Surface specified with parameters
denoted (s,t) and the partial derivatives are written out using the ∂-notation: ∂ r ∂ s , ∂ r ∂ t , ∂ 2 r ∂ s 2 , ∂ 2 r ∂ s ∂ t , ∂ 2 r ∂ t 2 . {\displaystyle
Parametric_surface
Problem in physics and quantum mechanics
Classical mechanics Old quantum theory Interference Fundamentals Bra–ket notation Complementarity Energy level Entanglement Hamiltonian Measurement Nonlocality
Many-body_problem
Notation in general relativity
(NP) formalism is a set of notation developed by Ezra T. Newman and Roger Penrose for general relativity (GR). Their notation is an effort to treat general
Newman–Penrose_formalism
American composer (1926–2002)
was a close associate of John Cage, and established his own formal and notational systems. As such, he created "open form,"[full citation needed] a style
Earle_Brown
Fictional character from The Legend of Sleepy Hollow
1812, whom he had met in 1814 in Sackets Harbor, New York. According to a notation by Irving and a certification written in longhand by Martin Van Buren,
Ichabod_Crane
Interpretation of quantum mechanics
Classical mechanics Old quantum theory Interference Fundamentals Bra–ket notation Complementarity Energy level Entanglement Hamiltonian Measurement Nonlocality
Many-worlds_interpretation
Linear regression model with a single explanatory variable
{Var} \left({\hat {\alpha }}+{\hat {\beta }}x_{d}\right)=\operatorname {Var} \left({\hat {\alpha }}\right)+\left(\operatorname {Var} {\hat {\beta
Simple_linear_regression
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
Linear function of explanatory variables used to predict a dependent variable
}}\cdot \mathbf {x} _{i}} using the notation for a dot product between two vectors. An equivalent form using matrix notation is as follows: f ( i ) = β T x
Linear_predictor_function
Quantum mechanical state change
Classical mechanics Old quantum theory Interference Fundamentals Bra–ket notation Complementarity Energy level Entanglement Hamiltonian Measurement Nonlocality
Spontaneous_emission
explorer Sir Edmund Hillary; a look at the use of computers for dance notation which record a dancer's movement; and a camera that can perform complex
List of The Nature of Things episodes
List_of_The_Nature_of_Things_episodes
Art of designing motion of physical bodies
also refer to the design itself, sometimes expressed by means of dance notation. Dance choreography is sometimes called dance composition. Aspects of dance
Choreography
notation (100) indicates that a batter scored 100 runs and was out. (100*) indicates that a batter scored 100 runs and was not out. Bowling notation (5/40)
Men's_T20_World_Cup_records
Physics phenomenon
formalism and theoretical framework developed in the articles bra–ket notation and mathematical formulation of quantum mechanics. Consider two arbitrary
Quantum_entanglement
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HAT NOTATION
HAT NOTATION
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HAT NOTATION
HAT NOTATION
HAT NOTATION
HAT NOTATION
HAT NOTATION
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