Identity Definition and 1000 Threads

Homework Statement Find a 2 by 2 matrix such that when cubed, is equal to the identity matrix. This matrix cannot be equal to the identity matrix unless it is cubed. So for example: B3 = [1 0;0 1] but B≠[1 0;0 1] The Attempt at a Solution The professor told us that we have to use a...

Homework Statement Which of following statements are TRUE or FALSE. Why? In any group G with identity element e a) for any x in G, if x2 = e then x = e. b) for any x in G, if x2 = x then x = e. c) for any x in G there exists y in G such that x = y2. d) for any x, y in G there exists z...

Homework Statement The context of the problem is that it's a vector valued function (VVF) problem where I'm supposed to sketch a curve generated by a VVF. To make the sketching easier I'm supposed to convert a VVF to a real valued function so that I can take advantage of the shape of a curve...

Let p_n be number of Non-Isomorphic Abelian Groups by order n. For R(s)>1 with \zeta(s)=\sum_{n=1}^{\infty}\frac{1}{n^s} we define Riemann zeta function. Fundamental theorem of arithmetic is biconditional with fact that \zeta(s)=\prod_{p} (1-p^{-s})^{-1} for R(s)>1. Proove that for R(s)>1 is...

How do (offshell) QCD ward identities look like in the axial gauge? How to derive them? The standard treatment of ward identities uses BRST symmetry in the covariant gauge. I don't know where I can read about the axial gauge version of the ward identities.

i am working on my expository research about integer sequences and their relationship with the pascal's triangle using the Lockwood's identity. but unfortunately i can't provide a complete proof for the said identity. please help me. I've been working on it for months but still i can't do the...

Homework Statement http://img39.imageshack.us/img39/4729/daumequation13275759907.png Homework Equations N/A The Attempt at a Solution Hmm... This is a tough one. I thought these two functions have been mathematically proven to be exactly the same? Does it have something to do...

So I have come across this integral identity in Krall's Principles of Plasma Physics (right after equ. 6.4.4 in the 1st edition) and I have not been able to show the identity is true. The reason that I would like to understand the integral is that I am trying to solve a similar problem to the...

Homework Statement Show that cosh^2(x) = (cosh(2x) - 1)/2 Homework Equations cosh(x) = (e^x + e^-x)/2 The Attempt at a Solution I have attempted this multiple times and get the same results every time. Squaring cosh(x) I get 1/4(e^2x + e^-2x +2), which is i believe 1/4(cosh(2x) +2)...

Does the definition of the vector triple-product hold for operators? I know that for regular vectors, the vector triple product can be found as \mathbf{a}\times(\mathbf{b}\times\mathbf{c})=( \mathbf{a} \cdot\mathbf{c})\mathbf{b}-(\mathbf{a}\cdot\mathbf{b})\mathbf{c}. Does this identity hold...

Homework Statement http://img843.imageshack.us/img843/3826/help3c.png Homework Equations Not applicable. The Attempt at a Solution http://img810.imageshack.us/img810/5577/help2n.png Can anyone prove this by evaluating the left side and right side independent of each other...

Hello, I am really familiar with the Ward-Takashi identity formulated in the form k_{\mu}M^{\mu\nu}=0 applying the fact that the longitudinal polarization of the 4 vector A is nonphysical (redundant) and should not contribute to the physical amplitudes. But, by opening a test subject on QED, I...

Trig identity with natural logs and absolute value?? Homework Statement -ln|csc(x) + cot(x)|= ln|cscx(x)-cot(x)| Homework Equations The Attempt at a Solution I got that csc(x)=1/sin(x) and cot(x)=cos(x)/sin(x), giving me a common denominator, added together I have...

Homework Statement Simplify: cos(4θ) Homework Equations cos(2θ)=2cos^2(θ)-1 sin(2θ)=2sinθcosθ The Attempt at a Solution First, I broke it into cos(2θ+2θ). Then I expanded it and got cos(2θ)cos(2θ)-sin(2θ)sin(2θ). I then expanded that and got...

Homework Statement cos(4x)(6+2a)+12a+8b=-20 find values for a, b. Then check the values and state which values of x would not have been sufficient checks. Homework Equations Complex number equations The Attempt at a Solution I've simplified it down to this from a harder problem...

Homework Statement Prove that, for all x, y \in \mathbb{R}, [2x] + [2y] \geq [x] + [y] + [x + y]. Homework Equations I am using [\cdot] to represent the floor function, and \{\cdot\} to represent the fractional part of a real number (\{x\} = x - [x] for real numbers x). We may...

Hello all, I am new to these forums, and I look forward to plumbing the depths of this interesting site. Anywho, I come to you with a bit of a potentially difficult question. I have always been immensely interested in Astronomy and Physics, and I decided long ago to pursue a career in either...

Homework Statement http://img829.imageshack.us/img829/3413/daumequation13237287425.png Prove that LS=RS. Homework Equations There are no relevant equations. The Attempt at a Solution http://img829.imageshack.us/img829/3413/daumequation13237287425.png

Homework Statement sin2x-tan2x=-2(sinx)^2(tan2x) 2. The attempt at a solution I have like two pages of attempts, but I don't know if it would be useful to copy it into the forum. :|

Homework Statement If I have a solution to a system of first order linear equations: <x,y> = c_1 e^{-3t} <1,-1> + c_2 e^{-t} <1,1> , how do I find the fundamental matrix psi(t) so that psi(0) = I ? Homework Equations The Attempt at a Solution psi(t) = <<e^{3t}, e^{-t}>...

Hi, How is \frac{1}{\displaystyle{\not}{P}-m+i\epsilon}-\frac{1}{\displaystyle{\not}{P}-m-i\epsilon} = \frac{2\pi}{i}(\displaystyle{\not}{P}+m)\delta(P^2-m^2) ? This is equation (4-91) of Itzykson and Zuber (page 189). I know that \frac{1}{x\mp i\epsilon} =...

Hi, I'm trying to prove the Shouten identity for twistors: \langle pq\rangle\langle rs\rangle+\langle pr\rangle\langle sq\rangle+\langle ps\rangle\langle qr\rangle=0 It's easy to show that the LHS here is cyclically symmetric under q\to r\to s \to q, and also completely antisymmetric...

Hi, I am trying to figure out what the result is when adding two sinusoids of the same frequency but with different phase and amplitudes. Specifically I want to know if the result is always another sinusoid of the same frequency. For the case of the the same amplitude I have: cos(wt) +...

Given vector spaces V, W over a field, and linear transformation T:V\rightarrow W, prove T(0_{v})=0_{w} where 0_v and 0_w are additive identities of V and W. I'm trying to use the definition of additive identity. So, \forall\vec{v}\in V,\vec{v}+0=\vec{v+0=0} . Where do I go from here?

Homework Statement I'm stuck on a question that results in this equality sin 2x = sin 2y how do I solve that for x or y? the only identity is the double angle one I can use I think but I don't know how that would help. Homework Equations The Attempt at a Solution

Homework Statement Let s*(f) be the minimum number of transpositions of adjacent elements needed to transform the permutation f to the identity permutation. Prove that the maximum value of s*(f) over permutations of [n] is {n \choose 2}. Explain how to determine s*(f) by examining f...

Please teach me this: Can we deduce Ward Identity in QCD from U(1) symmetry of QED?Because QCD is a theory of quarks and quarks have electric charge.So we need not deduce the Ward Identity from SU(3) symmetry,but we can be able to demontrate the Ward Identity( considering gluons)with U(1)...

Hi, I've come across the identity det(expA)=exp(Tr(A)) many times now, but recently came across log(detA)=Tr(log(A)), can anyone explain to me why this is true? or if it can be derived from the more familiar first identity? I'm not sure if there are any particular constraints the matrix must...

e^iA = cosA + i*sinA is true iff A is expressed in Radians. Why that particular unit? (I'm not sure this rubric is the right one for this question, but since it didn't seem to fit any of the other rubrics, I put it here.)

Hi, I am a engineering student and I am currently upgrading my maths level on my own to follow physics courses. While reading a book, I came across a vector differential identity that I don't manage to prove using index notation. The identity is the following: \nabla(\vec{A}\cdot\vec{B}) =...

I am sure that my questions are stupid. If we have a Hilbert space H, what do we mean by the closed subspace of H. Also, Does every Hilbert space have an identity? :P. Could anyone please clean to me these things . Thanks!

Homework Statement The question is to use index notation to show that the following is true, where a is a three-vector and f is some function. Homework Equations The Attempt at a Solution Hmmmm . . . I haven't really got anything to put here! I am starting to get to grips...

Homework Statement I missed one class on trigonometric identities in integrals, and I feel that one is needed here: \int^3_0\frac{1+arctan(\frac{x}{3})}{9+x^2}dxHomework Equations The Attempt at a Solution Again, I'm unsure what to do. I think that it is a trig identity, but I could be wrong...

So I am trying to follow my professors notes. Here is my work on the proof. And on the bottom is my answer and his answer. I know my answer is wrong, as I do not fully understand how to convert the summations at the end to their vector quantities. Is my work incorrect...

Homework Statement Show that (AB)^+ = A^+ B^+ using index notation Homework Equations + is the Hermitian transpose The Attempt at a Solution I know that AB = Ʃa_ik b_kj summed over k so (AB)^+ = (Ʃa_ik b_kj)^+ = Ʃ (a_ik b_kj)^+ = Ʃ (a_ik)^+(b_kj)^+ = A^+ B^+ I am not...

How do I prove that Ʃ\ket{ei} \bra{ei} = I

I just found out someone in my city signed up for phone service using my SS#. I owed $120. I got it cleared up, but it's scary. What else can they do!? :frown: I thinking of signing up at http://www.lifelock.com Anyone have opinions of that service?

Homework Statement Establish the identity: 1+cos(2θ)+cos(4θ)+cos(6θ)=4cosθcos(2θ)cos(3θ) Homework Equations cos(a)+cos(b)=2cos((a+b)/2)cos((a-b)/2) The Attempt at a Solution I understand how to do a simple cos(+/-)cos problem according to the Sums as Products equations, but I am...

Homework Statement Prove; \int_{-\infty}^{\infty} \frac{sin(\gamma)}{cosh(\lambda)-cos(\gamma)} e^{i \omega \lambda}d \lambda= 2 \pi \frac{sinh(\omega(\pi-\gamma))}{sinh(\pi \omega)} Homework Equations Contour Integration/Residue Theorem? The Attempt at a Solution I have messed...

Homework Statement Suppose f is one element of \mathbb{A}, and it has the property that f \circ g = g \circ f for every g \in \mathbb{A}. Prove that f = e (the identity function). Homework Equations \mathbb{A} = \{ g_{ab} : (a, b) \in \mathbb{R}^2, \, a \neq 0 \} g_{ab}(x) = ax + b The...

I am trying to follow a derivation in a book which is written without bra-ket notation, and presumably without the concept of state vectors. I can easily follow it if I may use the fact that \sum_{n}|\varphi_{n}\rangle\langle\varphi_{n}| is the identity operator. Analogously to the way I would...

I'm just wondering, is an identity matrix, say I3 considered as an elementary matrix? It's obviously possible, since we can multiply any row of I with a constant 1. I'm just curious if there is a restriction for rescaling with a constant 1.

I am trying to figure out a proof for this identity \nabla(f/g) = (1/g2) (g\nablaf - f\nablag) Any ideas?

Homework Statement Prove that for all positive integers n, the equality holds: SUM(nCk)*2^k=(3^n+(-1)^n)/2 Note: The sum goes from k=0 to n. AND k has to be even. Homework Equations Binomial Theorem The Attempt at a Solution I know that if we use the binomial theorem for x=2 and...

How would I go about showing \prod_{k=1}^{N-1} \sin{\frac{k\pi}{N}} = \frac{N}{2^{N-1}} I've tried using Euler's equation to substitute sin, but it just gets messy.

let be n and integer and 'i' the imaginary unit is then true that n^{ \frac{2i\pi n}{log}} =1 i believe that is true

Show that \displaystyle{\sum_{k=1}^{n-1}\sin\frac{km\pi}{n}\cot\frac{k\pi}{2n} = n-m}\quad\quad(m,n\in\mathbb{N}^+,\ m\le n)

Hello, I have the following equation in x and y: xy - \sqrt{(x^2+a^2)(y^2+c^2)} = -\frac{1}{a^2}-\frac{1}{c^2} where the quantities a2 and c2 are given real constants, and I have to find real values for x, and y such that the equation above is always satisfied. Actually, I know that the...

is this identity true? V is a vector, so VV is a second order tensor I have tried to prove this but the components of the tensor appear always as operands of the nabla. Thanks! Div(VV)=v.(Grad(V))

Homework Statement I just want to check if this identity is true, since I have not found it anywhere, can anyone help me? v is a vector (and that nu is supposed to be a v too)