Identity Definition and 1000 Threads

How to prove that ||An||=|A|n2? This property is used in my book but they did not give any explanation/proof of it. Can someone help? Edit: n2=n2

I'm working on simplifying a big physical expression (I don't like the Navier-Stokes equations at all anymore), and I'm curious how to simplify the following term: \vec{v}\cdot (\vec{v}\cdot\nabla )\vec{v} where v is a fluid velocity - i.e. definitely spatially varying. I'm just not sure...

Homework Statement Let \vec{A}(\vec{r})and \vec{B}(\vec{r}) be vector fields. Show that Homework Equations \vec{\nabla}\bullet(\vec{A}\vec{B})=(\vec{A}\bullet\vec{\nabla})\vec{B}+\vec{B}(\vec{\nabla}\bullet\vec{A}) This is EXACTLY how it is written in Ch 3 Problem 2 of Schwinger...

Homework Statement Verify C(n,k) = C(n-1,k) + C(n-1,k-1) algebraically. Homework Equations N/A The Attempt at a Solution I've set the identity up factorially like so: (n-1)!/k!(n-1-k)! + (n-1)!/[(k-1)!(n-2-k)! I'm having a really hard time getting started here. That is the...

I've been trying to find what the square of two cross products is and can't find it. Can anyone tell me the identity for (A X B)^2 ?

Homework Statement 2/(tanx+cotx)=sinx Homework Equations Double Angle Identities, Pythagorean Identities The Attempt at a Solution 2/(tanx+cotx)= 2/[(sinx/cosx)+(cosx/sinx)]= 2/[((sinx)^2+(cosx)^2)/(sinxcosx)]= 2sinxcosx/[(sinx)^2+(cosx)^2]= 2sinxcosx = sin(2x) =/=...

Homework Statement \cos (\frac{(-1)\pi x}{L})-\cos (\frac{3\pi x}{L}) Homework Equations The Attempt at a Solution the first cosine is the same as positive but is the second cosine simply equal to \cos (\frac{\pi x}{L})? thanks!

Homework Statement 3(sin(x)^4+cos(x)^4)-2(sin(x)^6+cos(x)^6)=1 (these are sinx raised to the 4 and 6 powers, not x^4or6) Homework Equations Pythagorean Identities The Attempt at a Solution I've tried using pythagorean identities to change everything to terms of sine or...

Homework Statement I was reading on the Weierstrass substitution, and I came across the following trigonometric identity: tan^{-1}(\alpha) - tan^{-1}(\beta) = tan^{-1}\left(\frac{\alpha-\beta}{1+\alpha \beta}\right)Homework Equations I'm not really sure which equations are applicable here...

Hi, I came across the following expression in Landau and Lifgarbagez's Quantum Mechanics (Non-relativistic Theory) book: \left(\cos\theta\frac{\partial}{\partial r} - \frac{\sin\theta}{r}\frac{\partial}{\partial\theta}\right)R_{nl}(r)Y_{l0}(\theta,\phi) =...

Homework Statement \sum_{i=0}^{n} i^{p} = \frac {(n+1)^{p+1}}{p+1} + \sum_{k=1}^{p} \frac {B_{k}}{p-k+1} (^{p}_{k}) (n+1)^{p-k+1} where Bk is a Bernoulli number. There is no actual question here I would just like to know if this formula is for sums of i to any power, of course...

Homework Statement Determine whether the operation has an identity element. x*y = 3xy Homework Equations e*x = x*e = x, if this holds, e is an identity element The Attempt at a Solution My attempt: x*z = z*x = 3xz, then 3xz = x <=> z = 1/3 => e = 1/3. But the answer key in the...

Suppose that f composed with g equals g composed with f for all functions g. Show that f is the identity function. I really just don't know where to start.

Homework Statement I am supposed to verify that \nabla\cdot(\mathbf{u}\times\mathbf{v}) = \mathbf{v}\cdot\nabla\times\mathbf{u} - \mathbf{u}\cdot\nabla\times\mathbf{v}\qquad(1)[/itex] I want to use index notation (and I think I am supposed to, though it does not say to explicitly) to...

Homework Statement Obtain the result of the infinite sum 1+\frac{1}{9}+\frac{1}{25}+\cdot\cdot\cdot By applying Parseval's Identity to the Fourier series expansion of 0 if -\frac{\pi}{2} < x < \frac{\pi}{2} 1 if \frac{\pi}{2} < x < \frac{3\pi}{2} Homework Equations...

Homework Statement Prove that for an integer n greater than or equal to 2, nC1 - 2nC2 + 3nC3 - + ... = 0. (nCm means n choose m) Also, 2x1 nC2 + 3x2 nC3 + 4x3 nC4 +... = n(n-1)2^(n-2) Homework Equations (1+t)^a = 1 + aC1(t) + aC2(t^2) + ... The Attempt at a Solution I don't know...

Does anyone know how to prove this? exp(jAt)+exp(jBt)= 2exp(j(A+B)/2)cos((A-B)/2)

1. Use Euler's identity to prove that cos3(t)=3/4cos(t)+1/4cos(3t) 2. ei\theta=cos(theta)+i*sin(theta) 3. 3/4cos(t)+1/2cos(3t)=3/4((eit+e-it)/2)+1/4((ei3t+e-i3t)/2)

Homework Statement [PLAIN]http://img812.imageshack.us/img812/4068/deriveidentitybydesmond.jpg In fact i came up with this identity just wondering if there is alternative way to prove it.Homework Equations The Attempt at a Solution

I'm reading through a solution to a problem and at one point the following identity is used: \frac{1-\cos(\beta)}{\sin(\beta)}=\frac{\sin(\frac{\beta}{2})}{\cos(\frac{\beta}{2})} I've been trying to figure out where this comes from but with haven't got it yet. Any ideas?

Hi, I've been trying to derive the electromagnetic stress tensor on my own, and I've run into a bit of a problem. I have a cross product of a curl (\vec{E}\times(\nabla\times\vec{E})) that I need to expand, and the typical...

Hey guys. How are you all doing? I'm helping my younger brother out with his trigonometry homework. He is dealing with verifying trigonometric identities. However, he has the problem that I am getting nowhere with. Hope you all can help. Thanks in advance. :) Homework Statement Verify...

Homework Statement the problem is: tan(theta) = cos(theta) find theta: -pi < theta < pi Homework Equations tan(theta)=sin(theta)/cos(theta) sin^2(theta)+cos^2(theta)=1 The Attempt at a Solution

Homework Statement Prove that if z=z(x,y) is invertible that: (dz/dx)(dy/dz)(dx/dy)=-1 where the d's represent partial differentiation not total differentiation Homework Equations The Attempt at a Solution I guess you start with the 6 total derivatives and substitute them...

Hello, I'm unfamiliar with the notation used in this problem with the commas. I understand matricies, identities, etc. but not sure about the commas.. Question 3.2.9: Verify the Jacobi Identity: [A,[B,C]] = [B,[A,C]] - [C,[A,B]] I see the BAC CAB rule here, but not sure how to show it...

1. I can't understand one step in the derivation of the Einstein tensor from the Bianchi identity.I have looked in a lot of books and all over the internet and everyone glosses over the same point as if its obvious, but it isn't obvious to me. 2. Below is the entire derivation. It seems...

Homework Statement Can anybody prove the following double integral identity? How?: \int_{0}^{1} s(1-s) f(sx) ds = \int_{0}^{1} s^2 \int_{0}^{1} t f(tsx) dt ds Here f(x) is an arbitrary Riemann-integrable function. Thanks in advance. Homework Equations I've found the following but it...

Is there an easy way to prove the identities: e^{\hat{A}}e^{\hat{B}}=e^{\hat{A}+\hat{B}}e^{[\hat{A},\hat{B}]/2} and e^{\hat{A}}\hat{B}e^{-\hat{A}}=\hat{B}+[\hat{A},\hat{B}]+\frac{1}{2!}[\hat{A},[\hat{A},\hat{B}]]+\frac{1}{3!}[\hat{A},[\hat{A},[\hat{A},\hat{B}]]]+...In Zettili they give that...

Homework Statement I have posted this problem on another website (mathhelpforum) but have received no replies. I don't know whether this is because no one knows what I am talking about or if it's just that no one can find a fault with my reasoning. Please please please could you post a reply...

Is the following property exclusive to the identity elements: a- = a (inverse of a = a)?

Homework Statement tanx=csc2x-cot2x Homework Equations Quotient, Reciprocal, Pythagoreans The Attempt at a Solution 1/sinx + 1/sinx - cosx/sinx - cosx/sinx = 2/sinx - 2cosx/sinx = (2-2cosx)/sinx STUCK~

Homework Statement Verify that \frac{Csc(x)}{Cot(x)+Tan(x)}=Cos(x) is an identity. Homework Equations All of the trigonometric identities. Sin^{2}+Cos^{2}=1; tan^{2}+1=Sec^{2}; 1+Cot^{2}=Csc^{2}; etc. The Attempt at a Solution I've literally written about five pages worth trying...

Hey all, hope you could help me, would be very gratefull if you could. Homework Statement Show that sin(x) + cos(x) = √2sin(x + π/4) Homework Equations sin(x+z) = sin(x)cos(z)+sin(z)cos(x) The Attempt at a Solution Ive been doing some of these trig identity problems without an...

Hello everyone, i was checking out a paper on simple rings http://www.imsc.res.in/~knr/RT09/sssrings.pdf and they said that all commutative simple rings are fields. i just don't see why they should have identity. thank you.

Homework Statement u and v are vectors Homework Equations show that : mod(u x v)^2 +(u.v)^2 = mod(u)^2 x mod(v)^2 The Attempt at a Solution I thought about let u =(a,b,c) let v = (x,y,z) and then doing the calculations. However I have done this but then squaring everything out...

Homework Statement In order to solve the problem I am working on, I have to prove the following generalized problem, S(x)=\sum_{n=0}^{\infty} n x^n =\frac{x}{(x-1)^2} for |x|< 1 I evaluated this sum using Wolfram Alpha. Clearly it looks related to the geometric series solution, but I am...

Do somebody knows anything about the Dirca's identity? \begin{equation} \label{Dirac} \frac{\partial^2}{\partial x_{\mu}\partial x^{\mu}} \delta(xb_{\mu}xb^{\mu}) = -4\pi \delta(xb_0)\delta(xb_1)\delta(xb_2)\delta(xb_3) \end{equation} here xb, is the 4-vector $x-b$ in Minkowsky spacetime...

Hey folks! I'm trying to figure out an identity from a paper on dimensional regularization. Here's the identity: -\frac{1}{2}\frac{d}{ds}|_{s=0}\int_0^\infty \frac{d^4k}{(2\pi)^4}(k^2+m^2)^{-s} after performing the k-integral this becomes...

Is it true that for all antisymmetric tensors F^{\mu\nu} the following identity is true: \nabla_\mu \nabla_\nu F^{\mu\nu}=0 (I've checked it but I'm not absolutely sure).

Homework Statement sin (x) + sin (3x) + sin (5x) + sin (7x) = 4cos(x)cos(2x)sin(4x) Homework Equations sin(a+b)=sin(a)cos(b)+sin(b)cos(a) sin(a-b)=sin(a)cos(b)-sin(b)cos(a) The Attempt at a Solution Me and four of my classmates have tried to do this proof and it kicked our ***...

vector identity?? Homework Statement The text that I'm reading has a line that reads \left(\mathbf{b}\mathbf{k}\cdot-\mathbf{b}\cdot\mathbf{k}\right)\mathbf{v}=\omega\mathbf{B} and I'm not sure what it means by \mathbf{b}\mathbf{k}; it's clearly not the dot product nor the cross product. A...

This is crazy. I have no idea what the textbook is saying at the end. So far, so good. Then this flies at me out of nowhere: We do?? Where the hell did that come from? I've never stared at something for so long without having the slightest clue what is going on. I held up the whole class...

Does x & y directions commute? Seem trivial! Just wondering whether any measurement made in the x direction affect it's y coordinate.

Homework Statement tan^2(x/2)=(sec x-1)/(sec x+1) Homework Equations The Attempt at a Solution

Are there any identities that are true for all real numbers, but not for all complex numbers? The only one I can think of is... \sqrt{ab}=\sqrt{a}\sqrt{b} Which is only true if a and b are POSITIVE, not real. But is there any identity that works for all real numbers, but fails for complex...

Homework Statement Prove the following identity: e^{x \hat A} \hat B e^{-x \hat A} = \hat B + [\hat A, \hat B]x + \frac{[\hat A, [\hat A, \hat B]]x^2}{2!}+\frac{[\hat A,[\hat A, [\hat A, \hat B]]]x^3}{3!}+... where A and B are operators and x is some parameter. Homework Equations...

Homework Statement Using index notation to prove \vec{\nabla}\times\left(\vec{A}\times\vec{B}\right) = \left(\vec{B}\bullet\vec{\nabla}\right)\vec{A} - \left(\vec{A}\bullet\vec{\nabla}\right)\vec{B} + \vec{A}\left(\vec{\nabla}\bullet\vec{B}\right) -...

Hi, I'm working my way through Schwinger's paper (http://www.physics.princeton.edu/~mcdonald/examples/QED/schwinger_pr_82_664_51.pdf" ) and I came across the following identity -(\gamma\pi)^2 = \pi_{\mu}^2 - \frac{1}{2}e\sigma_{\mu\nu}F^{\mu\nu} where \pi_{\mu} = p_{\mu} - eA_{\mu}...

let m,n be positive integer. Prove the identity: sum (i from 0 to k): { C(m, i) * C(n, k - i) } = C(m + n, k) Hint: Consider the polynomial equation: sum (k from 0 to m+n) {C(m + n, k) *z^k } = (1 + z)^(m+n) = ((1+z)^m) * ((1+z)^n) I tried long time, still have no idea.

Consider a binary operation on a set G. A an element e of G is said to be a left identity if ex=x for all x. If x is in G, an element y of G is said to be a left inverse of x if yx is a left identity. A right identity and right inverse is defined similarly. Is the following an adequate...