Notation Definition and 1000 Threads

In one of our lectures we wrote Maxwell's equations as (with ##c=1##) ##\partial_\mu F^{\mu \nu} = 4\pi J^\nu## ##\partial_\mu F_{\nu \rho} + \partial_\nu F_{\rho \mu} + \partial_\rho F_{\mu \nu} = 0## where the E.M. tensor is ## F^{\mu \nu} = \begin{pmatrix} 0 & -B_3 & B_2 & E_1\\ B_3 & 0 &...

There is some confusion regarding notation of the arguments of a probability distribution. For example, MLE is defined as estimating the distrubution that gives the maximum probability of the observations x_i given the distribution parameters, p(x|\theta) . However my instructor stressed that...

I've started Book of Proof, the first chapter of which is an intro to sets. Q.1 Is there any particular way to approach these kinds of problems, other than using intuition / trial & error? I tend to have some difficulty in working out the best way to express the general term of a sequence, for...

Hello! I have this problem: If H is a subgroup of prime index in a finite group G, show that either H is a normal subgroup or N(H) = H. What does N(H) means? I don't want a solution for the problem (at least not yet), I just want to know what that notation means. Thank you!

Just a couple of quick questions on index notation, may be because of the way I'm thinking as matrix representation: 1) ##V^{u}B_{kl}=B_{kl}V^{u}## , i.e. you are free to switch the order of objects, I had no idea you could do this, and don't really understand for two reasons...

Homework Statement Can I, for all purposes, say that Nabla, on index notation, is $$\partial_i e_i$$ and treat it like a vector when calculating curl, divergence or gradient? For example, saying that $$\nabla \times \vec{V} = \partial_i \hat{e}_i \times V_j \hat{e}_j = \partial_i V_j (\hat{e}_i...

Homework Statement I'm fully convinced that the zero values make sense, yet they are wrong, can somebody please explain why is that the case Homework Equations N/A The Attempt at a Solution Attempt in the image above

The material I am studying express the Ricci form as ##R = i{R_{\mu \bar \nu }}d{z^\mu } \wedge d{{\bar z}^\nu } = i\partial \partial \log G## where ##G## is the determinant of metric tensor, but I am not sure what does ##\log G## here, can anybody help?

Homework Statement Given that: g (1)=3 g (2x+1)=4g (x)+x+1 Find g (3) Homework Equations The awnser is 14. (Taken out of a PSAT workbook) The Attempt at a Solution I assume that g(2x+1) refers to a series of transformations (horizontal dilation, up 1) of g(x) Once g(x) is found, g(3) can...

I am following some lecture notes looking at the invariance of Poincare transformation acting on flat space-time with the minkowski metric: ##x'^{u} = \Lambda ^{u}## ##_{a} x^{a} + a^{u} ## [1], where ##a^{u}## is a constant vector and ##\Lambda^{uv}## is such that it leaves the minkowski...

let say I have a vector |a> and |b> and a transformation matrix A What is the difference between <a|A|b> and <a|Ab>? And also, I don't quite understand why <a|Ab> = <A+a|b>. Where does this identity come from? Thanks!

Hi. When referring to matrices what does ℝm x n mean ? Does this notation also apply to vectors ? Thanks

I'm working through some intro QFT using Peskin accompanied by David Tong's notes, and have a question over notation. From Peskin I have: x^\mu=x^0+x^1+x^2+x^3=(t,\mathbf{x}) and x_\mu=g^{\mu\nu}x^\nu=x^0-x^1-x^2-x^3=(t,-\mathbf{x}) so p_\mu p^\mu=g^{\mu\nu}p^\mu p^\nu=E^2-|\mathbf{p}|^2...

Homework Statement I am self studying relativity. In Wikipedia under the four-gradient section, the contravariant four-vector looks wrong from an Einstein summation notation point of view. https://en.wikipedia.org/wiki/Four-vector Homework Equations It states: E0∂0-E1∂1-E2∂2-E3∂3 = Eα∂α...

I am reading Louis Rowen's book, "Ring Theory"(Student Edition) ... I have a problem interpreting Rowen's notation in Section 1.1 Matrix Rings and Idempotents ... The relevant section of Rowen's text reads as follows: In the above text from Rowen, we read the following: " ... ... We obtain a...

I am reading Louis Rowen's book, "Ring Theory" (Student Edition) ... I have a problem interpreting Rowen's notation in Section 1.1 Matrix Rings and Idempotents ... The relevant section of Rowen's text reads as follows: In the above text from Rowen, we read the following: " ... ... We obtain...

Hi members, see attached PdF file. What's the difference between d/dx and d/d(x^2) I don't understand this notation?? Thank You

I'm having trouble in expressing the shaded region in set notation (Thinking) Many Thanks :)

The Poincare algebra is given by isl(2, R) ~ sl(2,R) + R^3. What exactly does the i stand for? Thanks a lot in advance!

I have just begun reading about Einstein's summation convention and it got me thinking.. Is it possible to represent ∑aibici with index notation? Since we are only restricted to use an index twice at most I don't think it's possible to construct it using the standard tensors (Levi Cevita and...

Is there some standardized math text with "proper universal notation" I could read for calculus? In one of my courses, $$\int\frac{dx}{x}$$ had a red mark through it, with a note that said "impossible" or something. I earned a zero on the question due to the above. In another instance...

Hello everyone. I have read a proof but I have a question concerning the notation. To give some context, I will write down this proof as written in the book. Theorem: There is a unique binary operation ##+: \mathbb{N} \times \mathbb{N} \rightarrow \mathbb{N}## that satisfies the following two...

Is the RHS of the conjugate relationship Ad(g)x = gxg-1 from the Lie algebra equivalent to: <g|λ|g> In the Dirac notation of quantum mechanics? I am looking at this in the context of gluons where g is a 3 x 1 basis matrix consisting of components r,g,b, g-1 is a 1 x 3 matrix consisting of...

{a,-a,0} ∈ Z For a set to have inverse under an operation, all elements must be able to be combined with another element of the set under that operation, after which the product of combination under said operation yields the identity element of that operation. My question is, this is a...

Homework Statement A) use sigma notation and calculate sum as far as you wish (set your own endpoint)(1/2) + (1/4) + (1/8) + (1/16)...B) this is a personal problem because I want to know how to calculate the sums with e.g. sigma notation, with a calculator. Never having done this before...

Hi everybody! The last chapter of my course named "Advanced Mechanics and Special Relativity" treats of Lorentz transformations, but the script of my teacher does not explain much about the notation used and it's getting quite confusing for me without understanding it fully. So far we've...

Homework Statement I shall be grateful if someone can help me understand this notation: http://files.engineering.com/getfile.aspx?folder=340bee11-1ba4-49b2-9a31-1a747012d69b&file=1.gif I know that this notation will finally/should finally give me the below six equations...

Homework Statement "For the given series, write formulas for the sequences an , Sn, Rn and find the limit as n->∞ (if it exists) Homework Equations ∑∞1 ((1/n) - 1/(n+1) The Attempt at a Solution I know how to take the limit, that's no problem. I'm a bit confused about what an , Sn, Rn are...

Hi PF! Which way is appropriate for defining del in index notation: ##\nabla \equiv \partial_i()\vec{e_i}## or ##\nabla \equiv \vec{e_i}\partial_i()##. The two cannot be generally equivalent. Quick example. Let ##\vec{v}## and ##\vec{w}## be vectors. Then $$\nabla \vec{v} \cdot \vec{w} =...

I have a question regarding the usage of notation on problem 2-11. Find ##f'(x, y)## where ## f(x,y) = \int ^{x + y} _{a} g = [h \circ (\pi _1 + \pi _2 )] (x, y)## where ##h = \int ^t _a g## and ##g : R \rightarrow R## Since no differential is given, what exactly are we integrating with...

Hi, while self-studying physics, I keep bumping into books that transition into more abstract math, using notation systems unfamiliar to me. This is often accompanied by explanations consisting of: 'we can write this as' 'it is easy to show that' 'therefore', which are not particularly...

I took a semester of QM as an undergrad engineering major, and I don't recall the motivation for replacing traditional vector notation with bracket notation. Can someone enlighten me? Thank you.

Hello. I am confused about the notation for tensors and vectors. From what I saw, for a 4-vector the notation is with upper index. But for a second rank tensor (electromagnetic tensor for example) the notation is also upper index. I attached a screenshot of this. Initially I thought that for...

If I have a scalar function of a variable ##x## I can write the derivative as: ##f'(x)=\frac{df}{dx}##. Now suppose ##x## is no longer a single variable but a vector: ## x=(x^1, x^2, ..., x^n)##. Then of course we have for the derivative ##(\frac{\partial f}{\partial x^1}, ..., \frac{\partial...

I am reading the proof of the Choi's theorem in his own paper. he first introduces ##E_{ij} ## as the nn null matrix but with a 1 at i,j. Then he uses ##(E_{ij})_{1<=i,j <=n}## he says that thi is a positive matrix. What is talking about? Is it a matrix of matrices?

This thread follows on from : https://www.physicsforums.com/threads/off-topic-maths-query-not-worthy-of-maths-forum.880724/#post-5534559 . Anybody ever used Polish notation or reverse Polish notation for computational formulae ? Use of either is supposed to eliminate ambiguity and make the...

I have reading through various sources on linear functionals, but all seem somewhat inconsistent with regard to denoting the set of all linear functionals and the set Also, what is the standard definition of a continuous linear functional? I really couldn't find much besides this Let ##f : V...

Can you help me figure out what the equation in the attached image means? What I do know is: h(p) is a Monge parameterization height function depending on radius (p), this is a boundary condition for a differential equation, and p0 is the outer boundary, with the inner boundary creating a...

Hi, Is the following notation correct? X = {xt> max(xt-k,...,xt-1,xt+1,...,xt+k)|(t-k,...,t+k) ∈ T2k+1∧ k ∈ ℕ\{0}} where T = [1,n]∩ℕ denotes the time periods over which x runs. I basically want to say that X is the set of points that are local maxima in a neighbourhood of k points to the right...

Hello, I've been studying spectroscopy in organic molecule and I came across an old data from 1934. 280(5b)(k,i±e), 297(1vd)(e), 354(1vd)(k,e), 378(1vd)(k,e), 398(Ovd) (e), 426(1vd)(k,e), 766(Ovd) (k,e), 807 (Od) (k,e), 817 (lb) (k,e), 842(1vd)(k,e), 862(2)(k,e), 878(3)(k,e), This is a piece...

What does the semicolon mean in the notation for a function like G(r1, r2; z) ?

I'm confused about the terminals in the picture above simply because I've seen the exact same thing mean 2 different things in schematics, namely: (1) it is an open circuit with voltage Vi(t) (2) The terminals are connected to some other circuit and thus have a voltage/current source, and the...

Is the chain rule below wrong? What I propose is as follows: Given that ##x_i=x_i(u_1, u_2, ..., u_m)##. If we define the function ##g## such that ##g(u_1, u_2, ..., u_m)=f(x_1, x_2, ..., x_n)##, then ##\frac{\partial g}{\partial u_j}=\sum_{i=1}^n\frac{\partial f}{\partial x_i}\frac{\partial...

Hi, i was just wondering if someone would be able to tell me what ωπ means when finding the gain and phase margins on a bode plot?

I have failed to Google the answer because I don't even know what to call it. You know that little "E" used in Engineering notation that lacks serifs? How do I make that "E"?

Homework Statement Use index and comma notation to show: \begin{equation*}\text{div }(\text{curl } \underline{\bf{v}}) = 0\end{equation*} Homework Equations \begin{align*} & \text{(1) div } \underline{\bf{v}} = v_{i,i} \\ & \text{(2) curl } \underline{\bf{v}} = \epsilon_{ijk} v_{j,i}...

Hi PF! Suppost I had some differential equation, say $$y'(x) + axy(x) +7a =0$$ where ##y=f(x)## and ##a## is some parameter. How do you reference this differential equation with different ##a## values are plugged in? Would I say $$ F(x,y;a) \equiv y'(x) + axy(x) +7a =0$$ and then when...

Homework Statement I'm trying to understand RSA and modular math better. I've studied some of the relations and rules, but I keep getting stuck when i try to follow an example all the way through. I'm also getting confused by how I'm supposed to treat ≡ vs = at some times. Here is the...

Homework Statement Find Fμν, given Fμν= (0 Ex Ey Ez) (-Ex 0 Bz -By) (-Ey -Bz 0 -Bx) (-Ez By -Bx 0) Homework Equations gμν =...

Hi All, Sorry, to begin with, if the question seems to be out of place. My question has to do with the notation (#) for the number of elements in a set: $$ N = \# \{ v_i \in V \vert v_i v_j \in E \} $$ Is it well known? If written in a scientific communication, must one offer a description of...