What is Notation: Definition and 1000 Discussions

In linguistics and semiotics, a notation is a system of graphics or symbols, characters and abbreviated expressions, used (for example) in artistic and scientific disciplines to represent technical facts and quantities by convention. Therefore, a notation is a collection of related symbols that are each given an arbitrary meaning, created to facilitate structured communication within a domain knowledge or field of study.
Standard notations refer to general agreements in the way things are written or denoted. The term is generally used in technical and scientific areas of study like mathematics, physics, chemistry and biology, but can also be seen in areas like business, economics and music.

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  1. J

    A Is the Dual Vector in Wald's Abstract Tensor Notation a Contraction?

    In Wald's "General Relativity", in his section on abstract tensor notation, he let's g_{ab} denote the metric tensor. When applied to a vector v^a, we get a dual vector, because g_{ab}(v^a, \cdot) is just a dual vector. Okay cool. But then he says that this dual vector is actually g_{ab}v^b...
  2. I

    A Lagrangian of a monopole (Einstein notation is used)

    Hi everyone, I am trying to calculate the equation of motion of a charged particle in the field of a monopole. The magnetic field of a monopole of strength g is given by: \textbf{B} = g \frac{\textbf{r}}{r^3} And the Lagrangian by: \mathcal{L} = \frac{m\dot{\textbf{r}}^2}{2} +...
  3. S

    Maxwell equations from tensor notation to component notation

    Homework Statement Verify that ##\partial_{\mu}F_{\nu\lambda}+\partial_{\nu}F_{\lambda\mu}+\partial_{\lambda}F_{\mu\nu}## is equivalent to ##\partial_{[\mu}F_{\nu\lambda]}=0##, and that they are both equivalent to ##\tilde{\epsilon}^{ijk}\partial_{j}E_{k}+\partial_{0}B^{i}=0## and...
  4. Drakkith

    I What is the Notation for Factorials?

    I just have a quick question on how to write the notation for a factorial. I have a series with a factorial of 5*10*15*...*(5n) in it. Is this written as 5n!, as (5n)!, or something else? I'm pretty sure it's 5n!, as I've written 5n! out as 5(1*2*3*4*...*n), which when you distribute the 5...
  5. Mr Davis 97

    I Question regarding the derivative terminalogy and wording

    When doing calculus, we typically say that we "take the derivative of a function ##f(x)##." However, rigorously, ##f(x)## is not a function but rather the value of the function ##f## evaluated at ##x##. Thus, in order for this wording to be correct shouldn't we have to write something like...
  6. smodak

    I Stupid Question about a Notation in Linear algebra

    I know the arrow -> means a map. For example, defines a linear map. But I cannot figure out what does a X mean? I know that above denote a inner product map. whatever is on the left of the : is defined by whatever is on the right. but what is the x symbol? What is the correct way to read...
  7. A

    I Subscript derivative notation

    I have an equation that looks like At, r = Aφ, r If I know that Aφ = r4 , then how do I find At ? I believe that the above equation is equivalent to: ∂/∂r (At) = ∂/∂r (Aφ) , correct? Then substitute the value Aφ and we have ∂/∂r (At) = ∂/∂r (r4) And then to get At I take the integral on...
  8. E

    Displacement operator, squeeze operator - problem interpreting notation....

    Homework Statement Prove the following relations (for ##\zeta:=r e^{i\theta}##): \begin{align} D(\alpha)^\dagger a D(\alpha)&=a+\alpha\\ S(\zeta)^\dagger a S(\zeta)&= a \cosh r- a^ \dagger e^{i\theta} \sinh r \end{align} Homework Equations ##|\alpha\rangle## is the coherent state. ##a## and...
  9. Kara386

    I Understanding Bra-Ket Notation in Quantum Mechanics

    In my lecture notes, it says that ##\left\langle l \right| A_{nm} \left| \psi \right\rangle = \sum_{n,m} A_{nm} \left\langle m \right| \left|\psi \right\rangle \left\langle l \right| \left| n \right\rangle## ##=\sum_{n,m} A_{nm}\left\langle m \right| \left| \psi \right\rangle \delta_{ln}## ##=...
  10. snoopies622

    I Confused about basis vector notation

    Why are basis vectors represented with subscripts instead of superscripts? Aren’t they vectors too? Isn’t a vector a linear combination of basis vectors (and not basis co-vectors?) In David McMahon’s Relativity Demystified, he says, “We will often label basis vectors with the notation e_a...
  11. S

    MHB Math Notation: How to explicitly specify the domain of a function symbolically?

    How can I specify the domain of a function symbolically? Assume I have a very simple linear function. $f(x)=2x$ If I want to say that the domain of this function is all the real numbers, how would I write this with symbols? Do I need to use set-builder notation? What would the set-builder...
  12. K

    I How do I convert [D]=[A][ B]T[C] to index notation?

    I am having trouble converting [D]=[A][ B]T[C] to index notation. I initially thought it would be Dij=AijBkjCkl but I have doubts that this is correct. Would anyone be able to elaborate on this? Regards
  13. P

    What do the numbers in front of electrolyte mixtures mean?

    Hello Everyone, I have a question about electrolytes. What do the numbers in front of the electrolytes mixtures mean? For example, let's say we have: 1EC:1DEC or 3EC:7EMC or 3EC:7EMC:1DMC Is that the volume fraction? If, I have for example 100 grams of 3EC:7EMC, would this mean 30 grams of...
  14. pellman

    B What does this set notation mean?

    $$ A \oplus B $$ where A and B are sets
  15. M

    I What is meant by this notation?

    when saying the probability distribution of X is f(x) = (3 x) this is to be like vector notation where 3 is above x but i can't write it like this here. what is meant by this notation ?
  16. T

    I Linear Transformation notation

    I'm confused about the notation T:R^n \implies R^m specifically about m. From my understanding if n=2 then (x1, x2). Are we transforming n=2 to another value m for example (x1, x2, x3)?
  17. G

    MHB Verifying Subgroup Notation of $H(x_0)$ in $A(S)

    Let $S$ be any set, $A(S)$ the set of one-to-one mappings of $S$ onto itself, made into a group under the composition of mappings. If $x_0 \in S$, what is meant by $H(x_0) = \left\{\phi \in A(S): x_0 \phi = x_0\right\}$? The set that contains the element $\phi$ in $A(S)$ that maps $x_0$ onto...
  18. A

    Solve Notation Puzzle: Vertical Bars in Equations Homework

    Homework Statement I have these two equations from this paper: https://www.scribd.com/doc/299960566/Spiral Homework Equations What are the vertical bars next to the drawn red starts supposed to indicate in this context? I'm trying to implement these equations into a program but I'm totally...
  19. Rococo

    Calculating <ψ(t)|x|ψ(t)> in a Harmonic Oscillator Potential

    Homework Statement A particle in a harmonic oscillator potential in the following state after a time t: ## | ψ(t) > = \frac{1}{\sqrt{2}} [e^{(-iE_0 t/\hbar)} |ψ_0> + e^{(-iE_1 t/\hbar)} |ψ_1> ] ## I want to write an expression for ## <ψ(t)| \hat{x} | ψ(t) > ##. Homework Equations The...
  20. Mrinmoy Naskar

    A good book for tensor notation....

    I am doing my M.sc in physics.. In my course I have classical field theory and electrodynamics... I need to learn tensor notations to understand the above subjects... Please tell me about some good introductory books to learn tensor notation to handle things in electrodynamics and classical...
  21. B

    What does the `|' represent in an infinite product notation?

    Hi, In my QFT course, the professor writes an infinite product like this: ∏n | k n0 > 0 ∫... My question is, what does the `|' in the subscript "n | k" representing? When I see `|', I think logical OR - obviously that is not it. Normally, if it's a sum over two indices, commas separate the...
  22. S

    Gradient of dot product using suffix notation

    Homework Statement Find the gradient of \underline{\nabla}(\underline{a}\cdot\underline{r})^n where a is a constant vector, using suffix notation and chain rule. Homework Equations On the previous problem,s I found that grad(a.r)=a and grad(r)=\underline{\hat{r}} The Attempt at a Solution...
  23. M

    MHB Quotient Groups & how to interpret notation?

    Hello, I am having some trouble truly interpreting what certain notation means when defining quotient groups, etc. (My deepest apologies in advance, with my college workload I simply have not had the time to really sit down and master latex.) Here are a few random examples I've seen in...
  24. P

    Vector calculus index notation

    Homework Statement prove grad(a.grad(r^-1))= -curl(a cross grad (r^-1)) Homework Equations curl(a x b)= (b dot grad)a - (a dot grad)b +a(div b) - b(div a ) The Attempt at a Solution Im trying to use index notation and get di (aj (grad(r^-1))j) =grad(r^-1) di(aj) +aj(di grad(r^-1))j which is...
  25. S

    Peskin and Schroeder - page 4 - choice of notation

    In page 4, Peskin and Schroeder has the following diagram: The diagram shows the collision of an electron beam and a positron beam to produce a ##\mu^{+}## beam a ##\mu^{-}## beam. My question is this: The electron and positron beams are shown to have momenta ##\textbf{p}## and...
  26. Clarky48

    Dirac notation - expectation value of kinetic energy

    It's my first post so big thanks in advance :) 1. Homework Statement So the question states "By interpreting <pxΨ|pxΨ> in terms of an integral over x, express <Ekin> in terms of an integral involving |∂Ψ/∂x|. Confirm explicitly that your answer cannot be negative in value." ##The 'px's should...
  27. KostasV

    Delta function and dirac notation

    Hello there ! I found this discussion http://physics.stackexchange.com/questions/155304/how-do-we-normalize-a-delta-function-position-space-wave-function about dirac notation and delta function . The one that answers to the problem says that ##<a|a>=1## and ##<a|-a>=0## . As far as i know: 1)...
  28. Isaac0427

    Notation for generalized coordinates

    I have seen both rk and qj both used to represent generalized coordinates in the Lagrange equations. Are these both the same things? Does it matter which you use? Thanks!
  29. TyroneTheDino

    Intro to abstract math—basic notation

    Homework Statement Simplify the following statement as much as you can: (b). ##(3<4) \wedge (3<6)## Homework Equations ##\wedge= and## The Attempt at a Solution I figured that I could just write this as ##3<4<6##, but then I considered what if I didn't know that ##4<6## If it was just...
  30. R

    Turbine performance: understanding notation

    Hi Guys. This is for my post graduation project. I came across a turbine performance map where the turbine specs are mentioned as GT12, 72 Trim, 0.39 A/R. Now what exactly these terms means. Please help.
  31. vabm

    Enunciation/notation in utility maximisation model

    Hi Everyone. I am working on a model that I think can be defined as a utility optimisation problem but I'm struggling with the enunciation and notation. The model should describe how the utilities of a set of agents A={1,2,...,n} increase with the availability of a larger set of product types...
  32. 5P@N

    What does this notation "<>" mean?

    So: what does "<>" mean?
  33. tomwilliam2

    Notation difficulties with metric and four vector

    I'm reading an introduction to relativity which uses different notation to the standard indices used in my college course. I came across: L(\nu)gL(\nu)g = 1 Where L is the Lorentz transformations four-vector and g is the metric. Without the indices, I'm a little lost. Is there some convention...
  34. P

    Correct mathematical notation for Volumetric Heat Capacity

    What is the correct notation for Volumetric Heat Capacity? I see it written both ways (Wiki for example). I'm pretty sure one is more correct but which is it? (1) Btu/ft³·°F or (2) Btu/(ft³·°F)
  35. J

    Relativity Mathematical Notation

    Homework Statement Find t(τ), x(τ), y(τ), z(τ) for constant electric field E=E(sinθx+cosθz) and B=Bz, and constant magnetic field where E,B, and θ are all constants. I haven't seen this notation before, and I really just want to know what it means specifically. I know and up indice paired...
  36. I

    Leibniz Notation: Understanding Diff. Calculus Anti-Derivatives

    The entire first semester of my Calculus class we used Lagrange's notation, f'(x), f''(x), etc.. So at the beginning of second semester the teacher kinda casually switched over to Leibniz notation, dy/dx, which left all of the class dazed. I understood it pretty well until she did a simple...
  37. xwolfhunter

    A question about the proper use of certain notation

    I'm currently reading a textbook for one of my classes (discrete mathematics), and we're doing set theory right now. This is not a question about how to do mathematics, it's about how to properly express through notation the concept I'm trying to convey. The text invites the reader to come up...
  38. X

    Adjoint operator in bra-ket notation

    Hi! First of all I want apologize for my bad english! Second, I'm doing a physical chemystry course about the main concepts of quantum mechanics ! The Professor has given to me this definition of "the adjoint operator": <φ|Aψ> = <A†φ|ψ> My purpose is to verificate this equivalence so i...
  39. ognik

    MHB Index notation determinant

    Making sure I have this right, $ |A| = \sum_{i}\sum_{j}\sum_{k} \epsilon_{ijk}a_{1i}a_{2j}a_{3k} $ (for a 3 X 3) and a 4 X 4 would be $ |A| = \sum_{i}\sum_{j}\sum_{k} \sum_{l} \epsilon_{ijkl} a_{1i} a_{2j} a_{3k} a_{4l} $ ? Is there any special algebra for these terms? (they could be...
  40. Paradox101

    Notation of mass number of an element

    In a lot of books I have seen the mass number of an element being written on left superscript of its chemical symbol,while my professor and other teachers write it in right superscript.However, it is written at the bottom of the symbol in the periodic table.Which is/are correct, or are all...
  41. G

    Advantage/disadvantage of notation

    When discussing Lorentz transformations some books use xμ/ = Λμ/αxα while some other books use x'μ= Λμαxα. Perhaps someone can help me understand which is the better notation. Thanks.
  42. I

    Values of ##k## for which ##A_{ij}A_{ij} = |\vec a|^2##?

    Homework Statement The antisymmetric tensor is constructed from a vector ##\vec a## according to ##A_{ij} = k\varepsilon_{ijk}a_k##. For which values of ##k## is ##A_{ij}A_{ij} = |\vec a|^2##? Homework Equations Identity ##\varepsilon_{ijk}\varepsilon_{klm} =...
  43. Chrono G. Xay

    Modulo Notation: Is There a More Efficient Way to Represent Modular Functions?

    Would it not be more efficient to write modular functions using the text formatting of logarithms? The modulus would be in subscript after "mod", and the expression to be used would be written after... Ex. modnf(x)
  44. C

    MHB Interval Notation of Inequality: -9<1/x<=1

    I need help determining the interval notation of the inequality below: -9<1/x<=1
  45. H

    A question on a notation used in hyperelastic literature

    Could someone please tell me what the tilde sign stands for in this equation:$$w_{0}\left(e_{ij}\right)=\int s_{ij}d\tilde{e_{ij}}=\frac{1}{2}\,\underline{\underline{s}}:\underline{\underline{e}}$$ where and ##\underline{\underline{e}}## is the Green Lagrangian strain tensor and...
  46. N

    Understanding Index Notation: Simplifying Tensor and Vector Equations

    Hello all, long time lurker, first time poster. I don't know if I am posting this in the proper section, but I would like to ask the following: In index notation the term σ_{ik}x_{j}n_{k} is \bf{σx}\cdot\bf{n} or \bf{xσ}\cdot\bf{n}, where ##σ## is a second order tensor and ##x,n## are vectors...
  47. M

    Identify Calculations & Prefix Notation

    Homework Statement https://i.imgur.com/U8muIJS.jpg[/B] Homework Equations Not aware of any equations required. The Attempt at a Solution For these questions I don't understand what I'm suppose to even. I have researched the terms prefix notation and Identifying calculations but after hours...
  48. R

    What is the meaning of g: [a, b] → R in set notation?

    I've been looking around a few places to try to understand some notation. I'm not sure exactly what to call it(set notation?) but basically things like g: [a, b] → R and stuff like that. I think it means something like g is defined on [a,b] in the real numbers, but is there a resource I can use...
  49. J

    Find Resultant Displacement Vector in Unit Vector Notation

    1. The problem statement, all variables and given/known dat A car travels 20 mi at 60 degrees north of west, then 35 mi at 45 degrees north of east. Express each displacement vector in unit vector notation. Take the +x-axis due east and the +y-axis due north. Use the component method to obtain...
  50. I

    How to Represent Eigenvectors in Column Matrix Form Using Bra-Ket Notation?

    I'm new to bra-ket notation and am slightly confused; given an infinite square well with eigenvectors: \phi = \sqrt{2/a}\sin( (n\pi x)/a) And we assume the form: H |φ> = E_n |φ> How would you then represent φ in terms of a column matrix, because that what I thought |φ> represents. Given...
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