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. nomadreid

    Adjacency matrices: (a) notation discrepancy, and (b) applications

    Two questions, both about adjacency matrices (graphs). The first, specific, the second, general. [1] I read: "Consider a directed graph and a positive integer k. Then the number of directed walks from node i to node j of length k is the entry on row i and column j of the matrix Ak..." [where A...
  2. E

    Help with Notation: Understanding x(.) & C(.)

    Having trouble understanding some notation: x(.) or C(.) (the dot is in fact in the center i.e mid-way vertically in the brackets). I have never run into this before? What does it mean if x is a function of "."?
  3. G

    Help with Lorentz Transformation Notation & Matrix Entries

    The symbol for a Lorentz transformation is sometimes Λαβ and sometimes Λμν. When Λαβ is shown by a matrix, the upper index denotes the entries in the rows and the lower index denotes the entries in the columns. When Λμν is shown by a matrix, does the upper index still denotes the entries in...
  4. S

    MHB Index Notation Proof: Proving $\nabla\cdot\left(\phi\textbf{u}\right)$

    Hi Everyone! I'm looking to prove $\nabla\cdot\left(\phi\textbf{u}\right)=\phi\nabla\cdot\textbf{u} + \textbf{u}\cdot\nabla\phi$ in index notation where u is a vector and phi is a scalar field. I'm unsure how to represent phi in index notation. For instance, is the first line like...
  5. N

    Analysis Notation Question

    The context is Tonelli/Fubini. What's the difference between saying ## y\mapsto\int_Ef^y(x)dx ## is measurable and ## \int_Ef^y(x)dx ## is measurable
  6. C

    Time Dilation Notation in SR: Clarifying the Differential Form

    So I have seen time dilation written as all three of the following: t=τγ, Δt=Δτγ, dt=dτγ. I'm assuming this not to be the case, but just wanted to clarify that the third (differential) notation does not imply that t=∫τγ? That really wouldn't make sense (to me at least), so I'm assuming that...
  7. S

    How BJT transistor works (with conventional current notation perspective)

    So far the explanation on BJT working principle always explained in electron flow perspective. I felt it's hard to relate with conventional current direction notation when the explanation explained in electron flow direction notation. For example in NPN transistor, the C-E current flow made me...
  8. I

    How about Why does the Landau notation for division work when h approaches 0?

    Why is it that, ## \frac{a+\mathcal{O}(h^2)}{b+\mathcal{O}(h^2)} = \frac{a}{b}+\mathcal{O}(h^2) ## as ##h\rightarrow 0##? It seems like the ##\mathcal{O}(h^2)## term should become ##\mathcal{O}(1)##.
  9. C

    Raychoudhuri's Equation in Abstract Notation

    In GR an important, purely geometric equation is called Raychoudhuri's equation governing the behaviour of geodesic congruences which states that $$\frac{d\theta}{d\tau} = - \frac{1}3 \theta^2 - \sigma^{ab}\sigma_{ab} + \omega^{ab}\omega_{ab} -R_{ab} u^a u^a$$ where ##R_{ab}## is the ricci...
  10. E

    Notation for Representing Arrays in Math Research

    I apologize if this is in the wrong forum, but I'm not quite sure there's a category where this would fit in. Anyway, I'm doing an independent research/analysis of the RGB color space, and as I'm writing down my formulas and algorithms, I want to express in the math that certain variables are...
  11. B

    How do I write a Cayley table for ##D_3## using cycle notation?

    Hello everyone, The problem I am working on asks me to write a Cayley table for ##D_3## using cycle notation. However, I am having difficult with determining how to operate on a pair of "cycles." Here is my work so far: ##R_0 = e = ()## ##R_{120} = (123)## ##R_{240} = (312)## ##F_T =...
  12. bcrowell

    Notational clash in index notation?

    Classical Theory of Particles and Fields, by Boris Kosyakov, has the following in appendix A: (I don't own a copy of the book. This came to my attention through this physics.SE question, and it turned out that this part of the book is accessible through Amazon's peephole.) This completely...
  13. andrewkirk

    Abuse of notation in relative homology theory

    I am refreshing my understanding of homology theory (well, recreating from scratch really!) after a thirty year break and there's something that bugs me in how the texts I've seen write about relative homology. The relative homology module ##H_q(X,A)## is defined as ##ker\ \partial_q^A/Im\...
  14. E

    Electron transition notation should be simple

    Alright, so I am trying to make sense of this notation: From one source I have the transition rates notated such as Transition: 2-1, 3-1, 3-2, etc and the source to which I want to compare uses the notation Transition: 3P0-3P1, 3P0-3P2, 3P0-1D2, etc. How are these related? How can I tell...
  15. K

    Help to understand the state notation

    Hi there, I am reading an article about the evolution of states. It is said that the system is initially in state |\Psi\rangle= a|a\rangle + b|b\rangle but after evolution, it becomes |\Psi'\rangle = a|a\rangle|c\rangle + b|b\rangle|d\rangle what is that (double ket) notation...
  16. mishima

    Help explain this Turing machine notation

    Below is an image from a website article discussing a Turing machine. It is supposed to represent a Turing machine, but I don't really follow the notation. I assume this is part of Wolfram's book, "New Kind of Science", which I do not have a copy of. I have only ever seen a Turing machine...
  17. CivilSigma

    Engineering Mechanics: Notation question

    In a problem involving moments where we have a 2 point is space: m and n. We want the moment about M due to a force applied at N. We know the equation is Moment = r (m/n) * F So, does r (m/n) represent the (x,y,z) coordinates from the point N to M or M to N?
  18. B

    Help with Index Notation: εlmn detA = εijkAilAjmAkn

    Homework Statement Show: εlmn detA = εijkAilAjmAkn Homework Equations not sure The Attempt at a Solution I'm really not sure where to begin. I understand index notation (at least I think I do). Can anyone help me get started? I think that once I have the first step, I'll be...
  19. DiracPool

    Integral Notation: Are ∫(x^2)dx & ∫dx (x^2) the Same?

    I'm confused over two different types of integral notation 1) ∫ (expression) dx and 2) ∫dx (expression) Are these the same thing? Example: Do ∫(x^2)dx and ∫dx (x^2) mean the same thing? Or is there a difference?
  20. B

    Difference between mixed tensor notation

    Hi, Can someone explain the difference between, say, \Lambda_\nu^\mu, {\Lambda_\nu}^\mu and {\Lambda^\mu}_\nu (i.e. the positioning of the contravariant and covariant indices)? I have found...
  21. M

    Looking for Continuum Mechanics book using Einstein Notation

    I'm taking a course in continuum mechanics this semester and the instructor is using a set of notes to teach out of it, problem is, I don't really like them. Can anyone recommend an engineering/applied physics oriented introductory continuum mechanics textbook that uses the Einstein summation...
  22. R

    Einstein notation and the permutation symbol

    Homework Statement This is my first exposure to Einstein notation and I'm not sure if I'm understanding it entirely. Also I added this class after my instructor had already lectured about the topic and largely had to teach myself, so I ask for your patience in advance... The question is...
  23. D

    Learn Einstein Notation with Examples and Notes

    Hi. Currently I'm taking an advanced particle physics course, and apparently Einstein notation takes up a lot in this course. Unfortunately for me, and several others in this course, we have never had anything with this kind of notation before. And pretty much from day one, we were put right...
  24. J

    Prove Vector Quadruple Product with Levi-Civita/Index Notation

    I'm asked to prove the following using Levi-Civita/index notation: (\mathbf{a \times b} )\mathbf{\times} (\mathbf{c}\times \mathbf{d}) = [\mathbf{a,\ b, \ d}] \mathbf c - [\mathbf{a,\ b, \ c}] \mathbf d \ I'm able to prove it using triple product identities, but I'm completely stuck...
  25. J

    Curl of a vector using indicial notation

    Homework Statement A.) Show that \epsilon_{ijk}A_{k,j} represents the curl of vector A_k B.) Write the expression in indicial nottation: \triangledown \cdot \triangledown \times A 2. The attempt at a solution I'm hoping that if I can get help on part A.) it will shed light on...
  26. Dethrone

    MHB Exploring $\equiv$, =>, and <=> Symbols

    First day of school and I don't have much work. So I got bored and read ahead a bit. From a textbook my prof wrote: Can someone explain why they used the "$\equiv$"? I think it means "equivalent", but I'm not sure, but when are times you want to use that symbol rather than "equals"? What's the...
  27. R

    Semiconductor Notation: P-Type, N-Type Band Gap Materials

    If you research the materials semiconductors are made of you will find things such as aluminum gallium arsenide. How do you determine what the p-type and n-type are made of? Shouldn't there be a structural difference in order to create band gap?
  28. P

    MHB Integral Notation Question

    I don't know if I've ever encountered a differential term with a modulus around it (or if I have, ignored it). Here's an example: $ \int\limits_{\gamma}{\rho(z)}{|{dz}|} $ If it was simply $ \int\limits_{\gamma}{|{dz}|} $ I imagine this is the length of the curve $\gamma $, but what might the...
  29. E

    MHB Notation for vector coordinates in a given basis

    Sorry for a long post. I am looking for a clear and concise way to explain how to compute coordinates when changes of basis or linear operators are involved. I would like to avoid the summation notation as much as possible and use the definition of matrix multiplication only in the beginning...
  30. Math Amateur

    MHB Left modules notation with a left subscript?

    I am reading Berrick and Keating's book on rings and modules. Berrick and Keating indicate a right module over a ring R as M_R, but in a left module the subscript is to the left ... can someone help me with the Latex script to achieve this? An example of "left-subscript" notation appears in...
  31. datafiend

    Pre calc review - interval notation

    Homework Statement What's the domain of 14/x2-x-6, in interval notation? Homework Equations \underline{14}x2-x-6 The Attempt at a Solution [3, + infinity) [-2,- infinity) Sorry, I can't find the infinity symbol Thx
  32. O

    Leibnitz's notation and derivatives of implicit functions

    First off: I think I understand the chain rule and how it derives from \lim_{h \to 0} \frac{ f(x+h)-f(x)}{h} and how to apply the chain rule when taking the derivative of an implicit function. The textbook I am reading Applied Calculus (by B. Rockett) uses the following example on...
  33. Roodles01

    Lorrentz force law & vector notation

    Homework Statement A current element is 3.0mm long, centerd on the origin of cartesian coordinates, and carries a current of 2.5A in the direction ez. What field does it produce at the point (3.0, 0, 4.0) Homework Equations This is obviously a Lorentz force law question so . . . ∂B =...
  34. D

    Any quick help with rearranging schrodinger equation in dirac notation

    I'm looking through my lecture notes, (studying relativistic corrections/perturbation theory using hydrogen), and I seem to have a mind block with one of the equations (the last one from the 3 in the middle). I know that the kinetic energy and coulomb potential has been subbed in for the...
  35. P

    What Are the Big-O Notations for n^(n-1) and (n-1)^n?

    Hi! For the following functions, what are their big-O notation? 1. n^(n-1) 2. (n-1)^n Should their big-O notations be the same as the original functions? i.e. 1. O(n^(n-1)) = n^(n-1)? 2. O((n-1)^n) = (n-1)^n? Please help! Many thanks!
  36. E

    Understanding Big O Notation: Limit Definition and Reconciling Statements

    I am trying to reconcile the following statement: " ||u||<=eps*||f|| means ||u||=O(eps) ("||u|| is order eps")... " with the limit definition of "big O"; considering it's not clear that ||u|| here even depends on eps: " lim as eps goes to 0 of ||u||/eps, by definition of "big O", should...
  37. J

    Is there a convention for horizontally shifting indices in tensor notation?

    Hi, I'm teaching myself tensor analysis and am worried about a notational device I can't find any explanation of (I'm primarily using the Jeevanjee and Renteln texts). Given that the contravariant/covariant indices of a (1,1) tensor correspond to the row/column indices of its matrix...
  38. dkotschessaa

    Notation Question (Differential Equations)

    I want to show, in a talk, how to build the Predator-Prey (Lotka Volterra) model. It starts off with the "Population Law of Mass Action" i.e. "At time t the rate of change of one population due to interaction with another is proportional to the product of the two populations at that time t"...
  39. G

    Good introduction for dirac notation

    Hi guys, I m reading some theoretical physics paper that requires knowledge of dirac notation if someone could point me out to a good tutorial on it I come from a math background but I am studying this paper with my supervisor.
  40. C

    Notation Question: Understanding "y --> 2^(-) implies y < -2

    Hi, I have a question about : http://imgur.com/RU7PvtJ I actually understand what I need to do. I need to see if both one sided limits are the same to establish that the limit exists. The only thing which I just find weird is the "since y --> 2^(-) implies y<-2" Can somebody explain me...
  41. Mandelbroth

    Notation for the Dual of a Vector Space

    I've been reading about algebraic geometry lately. I see that a lot of authors use ##V^\vee## to denote the dual space of a vector space ##V##. Is there any particular reason for this? The only reason I could think of is that this notation leaves us free to use ##R^*## to denote the units of...
  42. carllacan

    Notation for the nabla operator arguments

    Hi. In this development (c ∇+ d A)(c ∇+dA)= c^{2} ∇^{2} + d^{2}A^{2} + cd A∇ + cd ∇A (c ∇+ d A)^{2}= c^{2} ∇^{2} + d^{2}A^{2} + cd A∇+ cd A∇+ cd (∇A) I feel like we have "two" different ∇ operators. At the end of the first line ∇ acts on A and the test function (not shown). At the...
  43. BiGyElLoWhAt

    Question about notation in Linear Algebra

    Given vector spaces V, W, and a function T:V→W , state the two equations that the function T must satisfy to be a linear function. Does T:V→W mean a function that maps vectors in V into W? Or what does this actually mean?
  44. I

    Dirac notation Schwarz Inequality Proof

    Homework Statement This isn't really a problem so much as me not being able to see how a proof has proceeded. I've only just today learned about Dirac notation so I'm not too good at actually working with it. The proof in the book is: |Z> = |V> - <W|V>/|W|^2|W> <Z|Z> = <V - ( <W|V>/|W|^2 ) W|...
  45. Seydlitz

    Notation used in matrix representation of linear transformation

    Hello guys, Let ##T: \mathbb{R^2} \to \mathbb{R^2}##. Suppose I have standard basis ##B = \{u_1, u_2\}## and another basis ##B^{\prime} = \{v_1, v_2\}## The linear transformation is described say as such ##T(v_1) = v_1 + v_2, T(v_2) = v_1## If I want to write the matrix representing ##T##...
  46. gfd43tg

    Index notation matlab for 2D array

    Homework Statement Homework Equations The Attempt at a Solution Hello, I am having some confusion over the notation used in matlab. I don't really know what they mean A = [1:3; 4:6; 7:9] A = 1 2 3 4 5 6 7 8 9 A(1:2, 1:2) ans = 1 2...
  47. M

    Is 's' in Physics Notation Referring to Arc Length or Speed?

    Equation 1 ##\frac {d\vec T} {ds}## 2. s=arc length=∫|v|dt 3. |v|=speed 4. ds/dt = |v| (distance/time)Does the s from the notation of arc length or the notation of speed? derivative of arc length vs derivative of speed I am getting confused because ds was referred to as distance in a...
  48. T

    Index Notation & Dirac Notation

    Quantum Mechanics using Index notation. Is it possible to do it? I really don't get the Dirac Notation, and every-time I encounter it, I either avoid the subject, or consult someone who can read it. There doesn't seem to be any worthy explanation about it, and whenever I ask what is the Hilbert...
  49. R

    Is Λ the ∑ particle? or is Λ the Δ particle? notation clarification

    ive noticed some problems have the quark composition of Λ as uds, but in the Baryon Octuplet that is the same composition as ∑. I always thought Λ was another way of writing Δ, so the quark composition would be ddu, am I wrong?
  50. J

    What are the different forms of Fourier notation and how are they connected?

    The Fourier integrals and series can be written of 3 forms (possibly of 4): the "real cartesian": a(ω)cos(ωt) + b(ω)sin(ωt) the "real polar": A(ω)cos(ωt - φ(ω)) where: A² = a² + b² sin(φ) = b/A cos(φ) = a/A tan(φ) = b/a the "complex polar" A(ω)exp(iφ(ω))exp(iωt) And my...
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