# 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.

View More On Wikipedia.org
1. ### I Strange index notation for linear transformation matrix

I'm reading Liang's book on General Relativity and Differential Geometry, and came across this part: I just want to have a crystal clear understanding of why this notation is chosen. Basis transformation would be an automorphism from ##V## to ##V##, and there's a result saying that the set of...
2. ### B More convenient mathematical notation for a simple use case

So in my textbook there's a basic problem where you solve for the final velocities of two hockey pucks, which happen to have different colors which are red and blue, using conservation of momentum. The notation that the textbook uses to express the final velocities of the pucks is ##v_{1,f}##...
3. ### What does this derivative notation mean in Goldstein's Classical Mech?

My question is simply about the notation used here. What does $$F_s=-\frac{\partial V}{\partial s}$$ mean exactly?
4. ### I Is Diagrammatic Tensor Notation Widely Used in Mathematics?

Penrose demonstrates in his book "The Road to Reality" a "diagrammatic tensor notation", e.g., As I haven't seen it anywhere else, I wonder if anybody else uses it.
5. ### How to assign signs to energy?

The gravitational potential leads to velocity in downward direction, but spring potential does in upward direction. So should these energies have different signs (plus and minus or vice-versa)?
6. ### A On the group notation of the 1975 Wu-Yang paper

In the 1975 Wu–Yang paper on electromagnetism=fiber bundle theory Table 1: https://journals.aps.org/prd/pdf/10.1103/PhysRevD.12.3845 Wu & Yang use the notation ##\mathrm{U}_1(1)## for the bundle of electromagnetism and ##\mathrm{SU}_2## for the isospin gauge field. I am unfamiliar with this...
7. ### Understanding E subscript R Notation in the Context of General Relativity

All I know is that e subscript r must be a vector cos the book says so, but what does it mean, is it, a konstant in vector form? I'm confused by it (page one, chapter one spacetime and geometry by SeanCaroll) Help is appreciated Edit. Is vector r describing the curvature that takes place ?
8. ### What Does exp Mean in Mathematical Expressions?

In my introductory modern physics class, I was asked to compute the Taylor Series for exp(-ax^2) about the value x = 0 to second order in x. I am unfamiliar with the what "exp" before the function means, despite having approximated functions with Taylor Series before. I think there was some gap...
9. ### B Some questions regarding the integral of cos(ax), "a" not zero

Hi PF, $$\int \cos ax\,dx,\quad a\in{\mathbb R-\{0\}}\quad x\in{\mathbb{R}}$$ Let's make $$u=ax,\quad du=adx$$ and apply $$\int \cos u\,du=\sin u+C$$ $$\frac{1}{a}\int \cos ax\,adx=\frac{1}{a}\sin u+C$$ Substituting the definition of u $$=\frac{1}{a}\sin ax+C$$ Doubts: (i) Have I written well...
10. ### B Preference for the notation used for the wave function?

If I am correct, the wave function is presented as a vector in Hilbert Space. Alternatively this vector can be multiplied by the identity operator. Is there a preference for one notation or the other? Are they both possible representations of the same wave function?
11. ### I Difference between d/dt and d(theta)/dt? Why is it dr or ds/dt?

So, first of all, why and how are we taking the derivative of the vector r or s as d/dt if t is not a parameter of the equations? Second question is what is the difference between d/dt(r) and d(theta)/dt(r) and also between d/dt(s) and d(theta)/dt(s)? Like, both of these appear at the bottom of...
12. ### Notation for changing rows in a matrix

For this, What was wrong with the notation I used for showing that I has swapped the rows? The marker put a purple ? Any help greatly appreciated! Many thanks!
13. ### B Functions which relate to calculus: Questions about Notation

Hi. I'm self-studying functions which relate to calculus. Let me post what I feel I know and what I'm not grasping yet. Please correct any mistakes I'm making. I'm just talking real numbers: A function is a rule that takes an input number and sends it to another number. We can describe it...
14. ### I Tensor Calculus (Einstein notation)

Hello, I realize this might sound dumb, but I'm having such a hard time understanding Einstein notation. For something like ∂uFv - ∂vFu, why is this not necessarily 0 for tensor Fu? Since all these indices are running through the same values 0,1,2,3?
15. ### I Making Sense of Notation Confusion in Statistical Digital Signal Processing

I started my research in statistical digital signal processing two years ago, so I need to familiarize myself with all the notations people use in probability and statistics. I come from a deterministic science background. I name my variables based on what they mean. A velocity is a v , a...
16. ### I Dirac Notation for Operators: Ambiguity in Expectation Values?

Hi If A is a linear operator but not Hermitian then the expectation value of A2 is written as < ψ | A2| ψ >. Now if i write A2 as AA then i have seen the expectation value written as < ψ | A+A| ψ > but if i only apply the operators to the ket , then could i not write it as < ψ | AA | ψ > ? In...
17. ### I Bra-Ket Notation Manipulations: Quantum State Expansion

I suspect it will help if you know about my background: I did some linear algebra in university but never used it and am now in my mid 60s. I am interested in understanding the mathematics of quantum physics. I have read a number of layman's texts on quantum mechanics, but they all gloss over...
18. ### Calculators What is the meaning of this notation?

In hp 50g emulator, I performed this computation ## \lim\limits_{x\to\infty} [2^{2x} \times (\frac13)^x + (\frac12)^{2x}\times (\frac23)^x ]## What is the meaning of +:0 ?
19. ### I 4d integration/differentiation notation and the total derivative

This is probably a stupid question but, ## \frac{d\partial_p}{d\partial_c}=\delta^p_c ## For the notation of a 4D integral it is ##d^4x=dx^{\nu}##, so if I consider a total derivative: ##\int\limits^{x_f}_{x_i} \partial_{\mu} (\phi) d^4 x = \phi \mid^{x_f}_{x_i} ## why is there no...
20. ### I Consistent matrix index notation when dealing with change of basis

Until now in my studies - matrices were indexed like ##M_{ij}##, where ##i## represents row number and ##j## is the column number. But now I'm studying vectors, dual vectors, contra- and co-variance, change of basis matrices, tensors, etc. - and things are a bit trickier. Let's say I choose to...
21. ### B Beginner Einstein Notation Question On Summation In Regards To Index

So, I have recently been trying to learn how to work with tensors. In doing this, I have come across Einstein Notation. Below is my question. $$(a_i x_i)_{e}= (\sum_{i=1}^3 a_i x_i)_r=(a_1 x_1+a_2 x_2+a_3 x_3)_r$$; note that the following expression is in three dimensions, and I use the...
22. ### I From Einstein Summation to Matrix Notation: Why?

I know that if ##\eta_{\alpha'\beta'}=\Lambda^\mu_{\alpha'} \Lambda^\nu_{\beta'} \eta_{\alpha\beta}## then the matrix equation is $$(\eta) = (\Lambda)^T\eta\Lambda$$ I have painstakingly verified that this is indeed true, but I am not sure why, and what the rules are (e.g. the ##(\eta)## is in...
23. ### A Problem in Understanding notation of distributional section

In this post [Observables][1] By Urs Schreiber he denotes the space of distributional sections in defenition 7.9 by ##\Gamma_{\Sigma}^{\prime}\left(E^*\right) ## That is if ##u \in \Gamma_{\Sigma}^{\prime}\left(E^*\right)## than ##u## is a linear functional that takes as argument...
24. ### Proper Value Notation -- how to write VDC and VAC?

When specifying DC vs AC voltage excitation, is it appropriate to type 50 VDC with DC as a subscript? OR should it be "V DC"? The same concept if it were AC.
25. ### I What is this notation D|(n;n')|, and how to solve it?

I'm a beginner in the quantum mechanic and reading E. hill's paper explaining the intensity distribution of the doublet state for diatomic molecule (D->P). To calculate the intensities, D|(n;n')| and/or q(n,a,j;n'a',j') must be calculated, but I have never seen it before in linear...
26. ### I Question on bra vs ket notation

What's the difference between a bra vector and ket vector in specifying spin states except for notational convenience when calculating probablility amplitudes? Are they equivalent?
27. ### B Notation for infinite iteration

Hi Physics Forum, I want to ask if there is an "appropriate" notation for the infinite self-iteraction of an analytic function ##f(x)##, that is ##f(f(f(...)))##. For example I know ##f^{(+\infty)}(x)## can be a way, but there is an operator notation as for the infinite sum...
28. ### I Is my use of Einstein notation correct in this example?

I am wondering if I am using Einstein notation correctly in the following example. For a matrix ##R## diagonal in ##1##, except for one entry ##-1##, such as ##R = [1,-1,1]##, is it proper to write the following in Einstein notation: ##R_{\alpha} R_{\beta} = \mathbb{1}_{\alpha \beta} ##, such...

Why should it be ##\int_{a}^{x} f(t)dt## ? Couldn't it be like this: Let F(x) = ##\int f(x)dx## so ##\int_{a}^{x} f(x)dx## = F(x) - F(a) Thanks
30. ### I Dirac Notation for Vectors and Tensors (Neuenschwander's text ....)

I am reading Tensor Calculus for Physics by Dwight E. Neuenschwander and am having difficulties in confidently interpreting his use of Dirac Notation in Section 1.9 ... in Section 1.9 we read the following: I need some help to confidently interpret and proceed with Neuenschwander's notation...
31. ### Linear Algebra in Dirac Notation

I am trying to convert the attached picture into dirac notation. I find the LHS simple, as it is just <ψ,aφ>=<ψIaIφ> The RHS gives me trouble as I am interpreting it as <a†ψ,φ>=<ψIa†Iφ> but if I conjugate that I get <φIaIψ>* which is not equiv to the LHS. *Was going to type in LaTex but I...
32. ### Confusion about four vector notation

hi guys I am trying to learn special relativity and relativistic quantum mechanics on my own and just very confused about the different conventions used for the notation!?, e.g: the four position 4-vector some times denoted as $$x_{\mu}=(ct,-\vec{r})\;\;or\;as\;x_{\mu}=(ict,\vec{r})$$ or...
33. ### B Notation for a "scalar absolute field"?

The notation I think best describes it is ## F = \lVert\int^{space}_s|\vec{V}|ds\rVert ## So you have a vector field V in a 3d space. For each point you integrate over all of space (similar to a gravitational or electromagnetic field) *but* vectors in opposite directions do not cancel, they...
34. ### A Wald's Abstract Index Notation: Explaining T^{acde}_b

In the second paragraph on page 25 of Wald's General Relativity he rewrites T^{acde}_b as g_{bf}g^{dh} g^{ej}T^{afc}_{hj} . Can anyone explain this? I am confused by the explantion given in the book. Especially puzzling is that the inverse of g seems to be applied twice, which I can't make sese...
35. ### I Wavefunction in polar coordinates and its bra ket notation

The wavefunction of ##|\psi\rangle## is given by the bra ket ##\psi (x,y,z)= \langle r| \psi\rangle## I can convert the wavefunction from Cartesian to polar and have the wavefunction as ## \psi (r,\theta,\phi)## What bra should act on the ket ##|\psi\rangle## to give me the wavefunction as ##...
36. ### I Manipulation of 2nd, 3rd & 4th order tensor using Index notation

If I have an equation, let's say, $$\mathbf{A} = \mathbf{B} + \mathbf{C}^{Transpose} \cdot \left( \mathbf{D}^{-1} \mathbf{C} \right),$$ 1.) How would I write using index notation? Here A is a 4th rank tensor B is a 4th rank tensor C is a 3rd rank tensor D is a 2nd rank tensor I wrote it as...
37. ### B Confusion in notation of Lorentz Transformations

##\bar{\mathcal{O}}## is moving with a velocity ##v## relative to ##\mathcal{O}## along ##x^{1}## The Lorentz transformations between a Frame ##\mathcal{O}## and ##\bar{\mathcal{O}}## is given by: $$\Delta x^{\bar{0}} = \gamma\left(\Delta x^0 - v\Delta x^1\right)$$ \Delta x^{\bar{1}} =...

.
39. ### Notation clarification: SU(N) group integration

Hello, I would like help to clarify what det( {\delta \over \delta J}) W(J) (equation 15.79) actually means, and why it returns a number (and not a matrix). This comes from the following problem statement (Kaku, Quantum Field Theory, a Modern Introduction) Naively, one would define det...
40. ### A Re-writing the geodesic deviation eqn in matrix notation (3d only)

This is my attempt to re-write the geodesic deviation equation in the special case of 3 dimensions and +++ signature in matrix notation. We start with assuming an orthonormal basis. Matrix notation allows one to express vectors as column vectors, and dual vectors as row vectors, but by...
41. ### I A little clarification on Cartesian tensor notation

Goldstein pg 192, 2 edIn a Cartesian three-dimensional space, a tensor ##\mathrm{T}## of the ##N## th rank may be defined for our purposes as a quantity having ##3^{N}## components ##T_{i j k}##.. (with ##N## indices) that transform under an orthogonal transformation of coordinates...
42. ### I Notation of the approximation in quantum phase estimation algorithm

I'am interested in the notation of the approximation in quantum phase estimation algorithm. In the literature there are different definitions, which I divide into two cases here. Both different in their definition of the ##\delta##. In both cases I start with a quote of the source and show an...
43. ### Notation in fluid dynamics: A circle with a horizontal bar inside

I came across this notation when reading the wiki article on Venturi effect, which baffled me. Can someone please tell me its meaning?
44. ### A A better notation for a differential?

A ##\frac{df}{dx}## notation is problematic. Obviously, the letter 'd' has very different meaning when applied to the function or to the argument. Additionally, a separate letter '##\partial##' is used to denote a partial differential (a very rare case in math when a notation used for a general...
45. ### I What is unique about the bra in Dirac bra-ket notation?

It's said that every ket has a unique bra. For any vector ##|v> ∈ V## there is a unique bra ##<v| ∈ V*##. I'm not sure what that means. What is unique? Can anyone please help me understand. Thank you
46. ### I Issues on notation and concept of entanglement

As a follow up from my other thread, where I consider popular media describe entanglement sort of as: and I think this may be wrong. As a follow up question I want to put forward this: A singlet state of entangled particles is notated in a superposition of product states as: ##|up, down...
47. ### I Independent coordinates are dependent

(This is not about independence of ##q##, ##\dot q##) A system has some holonomic constraints. Using them we can have a set of coordinates ##{q_i}##. Since any values for these coordinates is possible we say that these are independent coordinates. However the system will trace a path in the...
48. ### I Question about L(v^2) Notation in Landau & Lifshitz's Mechanics

Hello : i am reading now landau & lifshitz book on mechanics and i have small question : about L(v^2) notation it was not very clear in the book and i couldn't understand it correctly anyone can explain it or provide a link with explanation page (4 - 5) Best regards Hagop
49. ### How to write this set in set-builder notation?

Homework Statement:: Write each of the following sets in set-builder notation. Relevant Equations:: None. {2, 4, 8, 16, 32, 64...} =2·{1, 2, 4, 8, 16, 32...} What should be the next step in this work?
50. ### Doubt related to notation used in writing Maxwell's equations

What does ##S=\partial V## and ##C=\partial S## signify, usually I have only seen books writing ##C## when evaluating a line integral over a curve ##C## and ##S## when evaluating a surface integral over a surface ##S##. Could someone clarify what ##\partial S## and ##\partial V## mean?