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. B

    Sigma Notation: Definition and Examples

    What does this mean? (see attachment) "Where b is a block defined by the contiguity condition c that may exist between elements of s, and n is the number of elements in that block" I know is not possible to get a solution without the actual function, but how does this reads?
  2. L

    Notation in linear algebra and rule for square of matrix norm

    Hi. I have a few simple questions. (<- sorry, please click this image.) 1. What does the notation in the red circle mean? 2. Is there a rule for expanding square of norm? (e.g. || A*B*C ||^2) I don't really understand how the first eq. changes to the second eq. Thanks. :)
  3. B

    A Little Trick for bra-ket notation over the Reals

    We know that < \phi | \psi >* = < \psi | \phi > where * denotes the complex conj. so if \psi and \phi are ordinary real valued functions (as opposed to matrices or complex valued whatevers) can we also say: < \phi | \psi > = < 1 |\phi \psi > = <\phi \psi | 1> Or what if \phi = \psi...
  4. A

    Solving Equations with Basic Math Notation

    When you start a new line in solving an equation (or any math problem), is there a symbol you should start of with? I usually use an equal or therefore sign but sometimes it doesn't seem appropriate and I just end up using a little arrow Say I had to rearrange this equation (ab)/2 = c to make...
  5. E

    Matrix notation - Two jointly Gaussian vectors pdf

    Hello I am having trouble deriving using block matrix notation the conditional pdf of two joint Gaussian vectors: I assume that it just involves some re-arranging of eq 1 (attatched) but am unsure if taking the inverse of the resultant matrix in eq 1 is valid and if the order of...
  6. N

    Anyone can help me on the chemistry notation

    I encountered a chemical (COOEt)2C, and I don't really know what does Et mean. I am not familiar with chemistry, but I guess this is something similar to -R which stands for -CH3, -CH2CH3 etc. Could anyone help to explain? Thanks you very much.
  7. Rasalhague

    What is the meaning of the shorthand notation used in dynamical systems?

    I have some questions about what I think is a fairly standard and common short-hand notation used in physics. Today I watched lecture 2 in the nptelhrd series Classical Physics by Prof. V. Balakrishnan. In it, he models a kind of system called a simple harmonic oscillator, I think using TC =...
  8. S

    Understanding Vector Notation: Solving Homework Equations

    Homework Statement Does r_{12} mean distance from point 1 to point 2, or point 2 to point 1?Homework Equations The Attempt at a Solution
  9. Saladsamurai

    What Is the Notation \text{OH}(X^2\pi - A^2\Sigma^+) Used For in Chemistry?

    Hi folks :smile: I really was not sure where to put this, so I put it here since it gets the most traffic. My friend is doing some experimental research on the concentration of hydroxyl radicals in flames. In the literature, she keeps encountering the notation: \text{OH}(X^2\pi -...
  10. W

    Help with Set-Builder notation

    Hello. Say that I want to express a set consisting of the values of a continuous function, G(x), over a range of integers. Is this a valid/acceptable format? \mathbf{G} = \{G(x) : \forall (x \in \mathbb{Z})(x \in [-range, range])\} or say that I want to express the vector formed by averaging...
  11. C

    Problems wiith the notation

    Hello, i have found a notation, which i never saw before and i can't give some reasonable definition for it. Perhaps some of you guys have seen it before and can help me. let k \in \mathbb{Z}^n and N be a constant, what does <k>^N mean? I will put more of the context, where this...
  12. G

    Which notation is the proper way to write vector quantities?

    What' the proper way to write vector notation? For a force... (10 N)i + (5 N)j + (6 N)k or are the brackets not standard and I can just go like this when I can indicate the superscript arrow above the unit vectors 10 Ni + 5 Nj + 6 Nk I'm not exactly sure and was hoping someone could tell...
  13. E

    Understanding Binomial PMF Notation: Clearing Up Confusion?

    Hi, could someone possible make something clear for me - I have come across this notation for a binomial PMF formed from an underlying beurnolli distribution: PS_{n}(\bar{p}n)\sim\sqrt{\frac{1}{2\pi n\bar{p}(1-\bar{p})}}exp [n\varnothing(p,\bar{p}] ,\\...
  14. P

    Change of variable for leibniz notation

    Hi I have a question for change of notation. Quote from textbook: As an example of a singular problem on a finite interval, consider the equation xy'' + y' + λxy = 0, (6) or −(xy')' = λxy, (7) on the interval 0 < x < 1, and suppose that λ > 0. This equation arises in the study of...
  15. L

    Index Notation and Kronecker Delta

    Homework Statement Simplify the following expressions involving the Kronecker delta in N dimensions. Where possible, write the final result without indices. C_{ns}\delta_{rn} Homework Equations The Attempt at a Solution I know Kronecker delta is symmetric but that doesn't seem to help. Is...
  16. M

    Find the Summation Notation and the Radius of Convergence

    Homework Statement Find the Summation Notation and Radius of Convergence of this series. 5, x, 10, x, ... The Attempt at a Solution I don't know how did they come up with that equation.. But the summation seems right.. Can anyone tell me how did they arrive with that equation? I've tried...
  17. R

    Electron Configuration - Notation Clarification

    Warm greetings, My confusion surronds Electron-orbitals... My text describes the sub-shells s, p, d, and f. If s shell has 2 electrons in spherical orbit, and p shell 6 electrons in 3 lobed orbitals, where on Earth are the other 2 electrons that complete the orbital shell of Neon? What is...
  18. O

    L&L - Elasticity - couple questions on notation

    Edit - maybe I have the notaton figured out now and am just confused. Homework Statement The below relevant quotations come from Landau and Lifgarbagez, volume 7 : The theory of elasticity, chapter 1. 2. Relevant quotations Page 2: where uik is the strain tensor, dl is the original...
  19. W

    Product Permutations/cycle notation

    Homework Statement This is just an example in a textbook but I'm completely stumped. This is dealing with cycles, and product permutations. So we have p=(341)(52) q = (1452) and we want to compute the product permutation qp Homework Equations so qp = (1452) * (341)(25) The...
  20. J

    What is Einstein Notation for Curl and Divergence?

    Anybody know Einstein notation for divergence and curl? What I would like to do is give each of these formulas in three forms, and then ask a fairly simple question; What is the Einstein notation for each of these formulas? The unit vectors, in matrix notation...
  21. T

    Notation (v*gradient operator)v in Navier-Stokes

    Notation "(v*gradient operator)v" in Navier-Stokes What does \left( \textbf{v} \cdot \nabla \right) \textbf{v} mean, assuming knowledge of the gradient operator? And, specifically, how would that be expanded? In general, I'm ignorant of the notation \left( f \left( y, \frac{d}{dx}...
  22. M

    Solve Differential Equation with Notation: Reduction of Order Help

    I need to solve the following differential equation, And am pretty sure it will require the use of Reduction of Order but have NO clue how do deal with the notation on the RH side, any help Would Be Greatly appreciated.
  23. Saitama

    Converting Sigma Notation: Simplifying Binomial Theorem

    Converting Sigma notation... Homework Statement (Not a homework question) Hi! I have been encountering problems in Binomial Theorem which includes converting the sigma notation. Like \sum_{k=0}^n \frac{n!}{(n-k)!k!} a^kb^{n-k}=(a+b)^n I got many questions in my exam of this type with four...
  24. C

    What is the meaning of 'x R x' and 'x R y --> x R z' in relation notation?

    Homework Statement Let R be a relation defined in a set A If for all x \in A we have x R x, we call R reflexive what does it mean when they write x R x ? And if for all x,y,z in A we have (x R y and y R z) --> x R z, we call R transitive . I am not sure what they mean...
  25. T

    Quadratic inequality-interval notation

    quadratic inequality--interval notation.. Homework Statement 2x^2<-x+10 Solve inequality and put into interval notation Homework Equations interval notation The Attempt at a Solution I don't even know where to start. I set it equal to zero -2x^2-x+10=0
  26. 0

    Dirac Notation and completeness relation

    I am confused about two minor things right now. The following illustrates both which I pulled from my QM book: <x|p_{op}|0>=\int_{-\infty}^{\infty}dp<x|p_{op}|p><p|0>=\int_{-\infty}^{\infty}dp~p<x|p><p|0>...
  27. Peeter

    Otimes notation and tau matrices used in definition of gamma matrices?

    In Zee's Quantum Field theory book he writes \begin{align}\gamma^0 &= \begin{bmatrix}I & 0 \\ 0 & -I\end{bmatrix}=I \otimes \tau_3 \\ \gamma^i &= \begin{bmatrix}0 & \sigma^i \\ \sigma^i & 0\end{bmatrix}=\sigma^i \otimes \tau_2 \\ \gamma^5 &=\begin{bmatrix}0 & I \\ I & 0\end{bmatrix}=I \otimes...
  28. J

    Function notation and inner product

    Homework Statement I have this problem, but I'm not familiar with the function notation that the professor is using. Can anyone tell me what is actually being asked? I understand everything up to the part that is in bold, but after that, I am lost. Some of the formating was lost so Rn is...
  29. M

    Calculating Force w/ Scientific Notation Answers Coming Out Wrong?

    This is a simple question. I am calculating the force of two masses based on the Universal Law of Gravitation. I am setting up the equation as G (gravitational constant of 6.67e-11)*mass1*mass2 all divided by the distance between the masses squared. This particular question is about masses...
  30. Z

    Understanding little-o notation

    I am currently reading Apostol volume 1, and I'm having trouble understanding little-o notation. I have searched the web for free resources, but can't find any. I don't quite understand his proof for theorem 7.8.e, and I don't understand his examples. For instance, why does \frac{1}{1 + g(x)}...
  31. H

    Matrix notation for vector stacking

    Hello, I have a row vector defined as, X=\{x_1,x_2,\ldots,x_L\} I wish to "stack" this vector vertically, a total of N times, such that the result is a matrix of the form, \begin{align}Y = \left[ \begin{array}{cccc} x_1 & x_2 & \ldots & x_L \\ x_1 & x_2 & \ldots & x_L \\ . & . & . & .\\ . & ...
  32. D

    Solving Tensor Notation Issue Homework

    Homework Statement I'm looking at the wikipedia article about four-momentum and I can't seem to get things right. It says Calculating the Minkowski norm of the four-momentum gives a Lorentz invariant quantity equal (up to factors of the ''c'') to the square of the particle's proper mass...
  33. W

    Euler-Lagrange equation in vector notation

    I read in hand and finch (analytical mechanics) that if you assume you have a lagrangian: L=(\phi,\nabla\phi,x,y,z) Then what does the euler lagrange equation look like in vector notation. I know that if you have a function with more than 1 independent variable then the euler-lagrange...
  34. N

    For the notation of Voltsecond and Volt-mu-second

    Homework Statement I have a question regarding the difference in the two notation found in the book, Switching Power Supply A to Z, on page 75(sorry I cannot show it here), It read something like this: We know that current swing is voltseconds per unit inductance. So we can also write...
  35. naima

    A question about index notation

    Could you please tell me what means B_{[ij} B'_{kl]} where B and B' are bivectors I found it in http://arxiv.org/abs/hep-th/0311162" look at lemma 2.4 thanks
  36. D

    Notation for basis of tangent space of manifold

    I sometimes see that the basis vectors of the tangent space of a manifold sometimes denoted as ∂/∂x_i which is the ith basis vector. what i am a little confused about is why is the basis vectors in the tangent space given that notation? is there a specific reason for it? for example, i know...
  37. I

    How abusive of notation is it to drop isomorphisms?

    I have a general sort of structural question. I have been reading a lot of maths papers lately, and it seems there are some isomorphisms that people omit from their calculations. For example, in a category with a terminal object, 1, A \cong A \times 1 where the isomorphism is given from left...
  38. S

    Correct Notation for Individual Ratios with Minimum Value | Help and Explanation

    Hi, Would this notation be correct, as regards to the use of "min"? X_i = \frac{A_i}{B_i}.min_i (\frac{A_i}{B_i}) I'm trying to say that for individual i the value of X is equal to that individual's ratio \frac{A_i}{B_i}, relative to the smallest ratio of all members of the group...
  39. N

    Notation question for Maxwell's Equations.

    I know I may be in the wrong place, but I think I'll get a quicker and better response here. My question is: How do \nabla \cdot \textbf{B} = 0 and \nabla \times \textbf{E} + \frac{\partial \textbf{B}}{\partial t} = 0 derive from \Box^2 A^\mu -\partial^\mu(\partial_\nu A^\nu) = j^\mu?
  40. J

    Set builder notation question.

    Homework Statement Use the set-roster notation to indicate the elements in each of the following sets. Homework Equations S = {n ∈Z |n(-1)k, for some integer k} The Attempt at a Solution Here is how I read this: "S is the set of all n’s that are a member of the integers...
  41. I

    Notation for Probability Distribution of Two Dice Rolls

    Hello friends, I have this problem it reads: A random variable X is defined to be the larger of the two values when two dice are thrown, or the value if the values are the same. Find the probability distribution for X. So I don't know how to state "X is defined to be the larger of the...
  42. Rasalhague

    Notation for Maps between Topological Spaces

    I'm used to the notation f : X --> Y for a map, where X and Y are sets. I recently came across this notation for a map between topological spaces, where the second item of each pair is a topology on the first: f : (X,{t}a) --> (Y,{tb}) Is the notation to be read "f maps each element of X...
  43. O

    Is there more than one meaning of the notation f(x)=[x] ?

    Is there more than one meaning of the notation "f(x)=[x]"? In my real analysis textbook there is a question that says: Decide whether f(x)=[x] is bounded above or below on the interval [0,a] where a is arbitrary, and whether the function takes on it's maximum or minimum value within that...
  44. Y

    How to denote tetrad in Abstract Index Notation ?

    I like Penrose's Abstract Index Notation very much. I am familiar with using Abstract Index Notation to denote Coordinate Basis. But when I try to denote tetrad with Abstract Index Notation, I meet problems. How to denote tetrad in Abstract Index Notation?
  45. A

    Statistics Notation: Mean, Variance & Normal Distribution

    In my lecture notes on confidence intervals the lecturer wrote this: I don't understand the notation of that bolded text. I know X is a random variable, μ is the population mean and σ is the population standard deviation but what does the ~ mean? Also the N(μ, σ2) I assume means normal...
  46. Z

    Why Use Odd Notation for Tensors in Linear Algebra?

    I've been looking through my notes for the last few weeks and i still do not see the reason for this use of notation that my lecturer uses, for example We denote by M^{*} \otimes M \otimes M^{*} the vector space of all tensors of type M \times M^{*} \times M \rightarrow \mathbb{R}, where M is...
  47. S

    How to Represent Set S to Distinguish a Single n from All Natural Numbers?

    G'day all, If i let S={[aij]nxn, where aij = aji, n\inZ+} How do I distinguish between a single natural number n or all natural numbers? I am trying to show that for each n, this set makes a subspace, but am not sure how to represent this set without the ambiguity, as this is not a subspace...
  48. C

    Any notation for component-by-component vector multiplication?

    I have a scalar function and a vector function and I need to make a scalar function as so: k=[kx ky kz] T=T(x,y,z) Function I want: div(k ? gradT) where "?" would be some operator that multiplies each component of k and gradT to make the vector [kx ∂T/dx , ky ∂T/∂y , kz ∂T/∂z] that way I...
  49. S

    Understanding Leibniz Notation: What does i=dq/dt Mean?

    I have a question I should have asked a LONG time ago. When we see this notation being used in such formulas as i=dq/dt (definition of current) or dy/dx (etc, etc), are we saying (in the case of current) that current is equal to the change in charge with respect to time? Or is it the "current...
  50. W

    Notation Question: Constraining N to an Interval [-a,+a]

    Hey all, I'm working on a derivation at the moment and I'm just wondering how I can write this mathematically. I've attached by current attempt (see attachment). What I'm trying to say is: N is an integer and is constrained to an interval of [-a,+a], where a is real. Is my 'syntax'...
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