Transformation Definition and 1000 Threads

Homework Statement Let us study the subgroup of the Poincare group that leaves the point ##x=0## invariant, that is the Lorentz group. The action of an infinitesimal Lorentz transformation on a field ##\Phi(0)## is ##L_{\mu \nu}\Phi(0) = S_{\mu \nu}\Phi(0)##. By use of the commutation...

Hi! I'm having problems with this homework my professor gave us this morning: Prove that Maxwell's equations is invariant under Lorentz Transformation. I'm just currently in third year, and we haven't been taught tensors yet. The extent of what I know mathematically is only until gradient...

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##...

I really don't understand what it is and what is the use of constant, like in this equation of transformation. x=k(x' + vt). The equation can also be good if it is just like this, x=x' + vt Thank you.

To=(time of moving object.) T=(Time of standing object.) ^=power of number. sqrt=square of number.(x^1/2)Law of einstein say: T= To / ( sqrt( 1 - u^2/c^2 ) ) Lorentz law say: T= (To + u*Xo/c^2) / ( sqrt( 1 - u^2/c^2 ) )Why there is difference?? Is for other things?? I thought is for the same...

Homework Statement This complies when I type it in my Latex editor, but not on here. If you could either let me know how to fix that or copy and paste what I have into your own editor to help, that'd be great. Thanks! While Ryder is setting up to derive a transformation rule for Dirac...

I have doubts regarding a statement related to the following proposition: Let ##(V,<,>)## be a finite dimensional vector space equipped with an inner product and let ##f:V \to V## be a linear transformation, then the following statements are equivalent: 1)##<f(v),f(w)>=<v,w>## for all ##v,w \in...

See: http://en.wikipedia.org/wiki/Y-%CE%94_transform#Basic_Y-.CE.94_transformation Is possible to express the following relationships: using matrix?

A variant of a problem from Halmos : If AB=C and BA=D then explain why (C-D)^2 is commutative with all 2x2 matrices if A and B are 2x2 matrices. This result does not hold for any other nxn matrices where n > 2. Explain why. Edit: I tried to show that ((C-D)^2) E - E((C-D)^2) is identically...

Homework Statement Find Möbius transformation that maps: a) circle ##|z+i|=1## into line ##Im(z)=2## b) circle ##|z-i|=1## into line ##Im(z)=Re(z)## c) line ##Re(z)=1## into circle ##|z|=2##Homework Equations ##f(z)=\frac{az+b}{cz+d}##The Attempt at a Solution a) Firstly to move the circle...

Hi All, I think I have confused myself ... perhaps you can tell me where my reasoning is wrong. The idea is that in general coordinates the partial derivative of a vector, \frac{\partial A^i}{\partial x^j}, is not a tensor because an additional term arises (which is the motivation for...

Is it true that there always exist a unitary matrix that can take a state vector of an arbitrary pure state to another arbitrary pure state ? (of course assuming same hilbert space). If true, how do we prove it ? it look like it is true via geometrical arguments but i have not been able to...

Homework Statement Let B = {(1, -2),(2, -3)} and S be the standard basis of R2 and [-8,-4;9,4] be a linear transformation expressed in terms of the standard basis? The Attempt at a Solution 1) What is the change of basis matrix PSB ? 1,2 -2,-3 2)What is the change of...

How can I geometrically interpret this coordinate transformation (from x,y space to \check{x},\check{y} space)? x = \check{x}cos(β) - \check{y}sin(β) y = \frac{1}{2}(\check{x}2 -\check{y}2)sin(2β) -\check{x}\check{y}cos (2β)

Let L: R3 -> R3 be L(x)= \begin{pmatrix} x1+x2\\ x1-x2\\ 3x1+2x2 \end{pmatrix} find a matrix A such that L(x)=Ax for all x in R2 From what I understand I need to find the transition matrix from the elementary to L(x). However it is'nt a square matrix and it has variables instead of numbers...

Homework Statement a) Determine power series ##\sum _{n=0}^{\infty }a_nt^n## if you know that its laplace transformation is ##-s^{-1}e^{-s^{-1}}## b) Determine function ##g## that this power series will be equal to ##J_0(g(t))##Homework Equations The Attempt at a Solution Hmmm, I am having...

Homework Statement Let ##y_1^{'}+y_1=y_2##, ##y_2^{'}+5y_2=y_3##, ##y_3^{'}+y_3=f## and ##y_1(0)=y_2(0)=y_3(0)=0##. Find ##Y_1(s)## in terms of ##F(s)##. Homework Equations The Attempt at a Solution I am completely lost here. I tried to rewrite the system so that I would...

Homework Statement Find Laplace transformation for functions ##f(t)##: a) ##5cos(7t+\pi /4)## b) ##e^{3t}sintcost##Homework Equations The Attempt at a Solution a) I know that for ##cos(\omega t)## the laplace is ##\frac{s}{s^2+\omega ^2}## but what can I do with that ##\pi /4## ? I believe I...

hello i want to derive the Transformation of acceleration between two reference frames i searched in internet and found a book but i don't understand just one step i attach a picture so you can see what i found in the internet my problem is eq. (1.10) \begin{align}du=\frac{dU}{\gamma...

Homework Statement utt=a2uxx Initial conditions: 1)When t=0,u=H,1<x<2 and u=0,x\notin(1<x<2) 2)When t=0,ut=H,3<x<3 and u=0,x\notin(3<x<4) The Attempt at a Solution So I transformed the first initial condition \hat{u}=1/\sqrt{2*\pi} \int Exp[-i*\lambda*x)*H dx=...

I have a linear transformation, T, from P3 (polynomials of degree ≤ 3) to R4 (4-dimensional real number space). I have a second linear transformation, U, from R4 back to P3. In the first step of this four-step problem, I have shown that the composition TU from R4 to R4 is the identity linear...

Let there be a triangle with coordinates A(2,2) , B(5,2) and C(5,4) I have learned two ways to shear an object(x-axis invariant) in the Cartesian coordinate system. The first way is to find the coordinate vector of a point and multiply the y-component of the vector by the shear factor(2)(Don't...

Homework Statement A girl is riding a bicycle along a straight road at constant speed, and passes a friend standing at a bus stop (event #1). At a time of 60 s later the friend catches a bus (event #2) If the distance separating the events is 126 m in the frame of the girl on the bicycle...

Homework Statement Given a transformation of the plane F(x,y) = (2x+y,x-2y), find F-1. Homework Equations Actually this exercise had an item (a) which I had to prove this is a transformation. So I proved this function is injective and surjective. I know F(x,y) = (u,v) IFF F-1(u,v) =...

Umm what just happened? I understand as far as u=x+y and v = y/x and when he does the 2d curl. What I don't get is the step thereafter when he flips it. How does he know to flip it? Further, when he flips it wouldn't that make the dvdu inside the integral cancel and hence leave him with dxdy?

Homework Statement Homework Equations The Attempt at a Solution What I don't understand is how I'm supposed to find those limits for U and V. That's not at all what I'm getting. I've tried solving for the max and min x,y coordinates from the given graphs but that doesn't yield...

So i am working on a question, which is beyond my knowledge of Lorentz transformations and some help is greatly appreciated. I have a 4 velocity, u=γ(v vector,c) and its transformation properties are the standard lorentz boost. I don't quite understand how I am supposed to do this given that...

Is the transformation of an operator under INFINITESIMAL unitary transformation, U^-1AU or UAU^-1?? I saw that two books defined it differently?

Homework Statement The Attempt at a Solution I don't think I'm interpreting the question correctly. Maybe someone can point me in the right direction? There are 2 conditions: if y =/=0 then f(x,y) = x^2/y and if y=0 then f(x,y) = 0 Let u =(1,1) and v = (1,1) f(v) = f(1,1) =...

Homework Statement f(x,y) -> |x+y| The Attempt at a Solution The answer is that the above transformation is not linear but my working shows otherwise. Here's my go: let u = (1,1) and v = (1,1) f(u) = f(1,1) = 2 f(v) = f(1,1) = 2 f(u) + f(v) = 4 f(u+v) = f(2,2) = 4...

Homework Statement Given below are three geometrically defined linear transformations from R3 to R3. You are asked to find the standard matrices of these linear transformations, and to find the images of some points or sets of points. a) T1 reflects through the yz-plane b) T2 projects...

Algorithms like the transformation algorithm: $(x, y)$ --> $(\frac{x}{k} + p, ay + d)$ are not generally used in mathematics. Instead, we use matrices. Multiplying matrixes: you multiply a row of the first matrix by a column of the second. Use the following example: $ \begin{bmatrix}x & y...

Homework Statement Find the standard matrix of the following linear transformation: T(x1, x2, x3, x4) = (-2 x1 - 5 x2 - 4 x3 - x4, 2 x1 + 2 x2 - 5 x3 + x4) The Attempt at a Solution [x1,x2,x3,x4] [-2,2;-5,2;-4,-5;-1,1] =[-2 x1 - 5 x2 - 4 x3 - x4, 2 x1 + 2 x2 - 5 x3 + x4]...

Mod note: fixed an exponent (% --> 5) on the transformation definition. Homework Statement A is a (4x5)-matrix over R, and L_A:R^5 --> R^4 is a linear transformation defined by L_a(x)=Ax. Find the basis for the range of L_A. Homework Equations The Attempt at a Solution ##A =...

Suppose we do a constant Jacobian transformation (which is not Lorentz) of a SR (inertial) frame, by using four linear change of variables equations. This defines an apparent field with a constant metric (which is not the SR metric) in which there is relative acceleration of separation. From...

Assume that, in cartesian coordinate, we have a quark with momentum ##k=(k_0,0,k_0sin\theta,k_0\cos\theta)## and a fragmented hadron ##p=(p_0,0,0,p_0)##. Define, in light-cone coordinate, ##k^+ = k_0 + k_3 = k_0(1+cos\theta)##, and ##p^+ = p_0 + p_3 = 2p_0##. And the longitudinal momentum...

Homework Statement Consider a ##j=1, SU(2)## representation (or fundamental ##S0(3)## representation). Suppose that ##a_i, b_i## and ##c_i## (i=1,2,3) are vectors transforming under this representation i.e ##a_i' = [\rho_1 (x)]_{ij} a_j = \rho_{ij} a_j## and similarly for b and c. Consider...

Homework Statement Find the Mobius transformation which carries the points 0,1,-i to the points -1,0,\infty respectively. Find the image of the domain \{z:x<0,-x+y<t\} under this mobius transformation.Homework Equations The Attempt at a Solution Let T(z)=\frac{az+b}{cz+d}. Then...

Homework Statement T4 : R3 -> R4 is defined by T4(x1, x2, x3) = (0, x1, -3 + |x1|, x1 + x2) The Attempt at a Solution I know that T4(γ1x1 + γ2x2 + γ3x3) is a linear transformation IFF γ1.T4(x1) + γ2.T4(x2) + γ3.T4(x3) T4(λ10 + λ2x1 + λ3(-3+|x1|) = λ1.T4(0) + λ2.T4(x1) +...

T2 projects orthogonally onto the xz-plane T3 rotates clockwise through an angle of 3π/4 radians about the x axis The point (-3, -4, -3) is first mapped by T2 and then T3. what are the coordinates of the resulting point? this question is on a program call Calmaeth. My answer for this...

v=? delta what/which X(distance) over delta what/which T(time) http://en.wikipedia.org/wiki/Special_relativity

Homework Statement Say if f is a linear transformation from R2 to R3 with f(1,0) = (1,2,3) and f(0,1) = (0,-1,2). Determine f(x,y). The Attempt at a Solution I understand the theorem on linear transformation and bases but unsure as to how I should apply it in practice. Should I be...

Homework Statement We have seen that the linear transformation ##T(x_1,x_2)=(x_1,0)## on ##\mathcal{R}^2## has the matrix ##A = \left( \begin{smallmatrix} 1&0\\ 0&0 \end{smallmatrix} \right)## with respect to the standard basis. This operator satisfies ##T^2=T##. Prove that if...

Homework Statement Image Attached Homework Equations Ohm's The Attempt at a Solution Combined the two resistors in series : 250 + 550 = 800 kΩ Source Transformation (Current Source): V = 140,000(2*10^-6)= 0.28 V Combine the voltage sources : 6 - 0.28 = 5.72 V But then I...

Homework Statement Frame S' travels at speed V1 along the x-axis of frame S. Frame S'' travels at speed V2 along the x' axis of frame S'. Apply the Lorentz transformation twice to find the coordinates x'', y'', etc of any event in terms of x, y, z, t. Show that this is the same as the...

In an exercise I am asked to find the eigenvalues of a matrix A by demanding that a unitary matrix (see the attached file) diagonalizes it. I know I could just solve the eigenvalue equation but I think I am supposed to do it this rather tedious way. Now I have introduced an arbitrary unitary...

Homework Statement Ok this might be a stupid question, but: https://fbcdn-sphotos-h-a.akamaihd.net/hphotos-ak-frc3/t31/q77/s720x720/10001118_10202561443653973_1625797585_o.jpg Why is this the case? I think for all of this to be right, then the assumption of ##Y=u(X) \Leftrightarrow...

Hello everyone. Sorry if the question is silly, but in really need to know something. We know that The Fourier transform of time is frequency and the inverse of frequency is time. In Matlab can anyone tell me how to write it ? Because in the book Non linear fiber optics by Agrawal we found that...

Homework Statement Homework Equations The Attempt at a Solution What is M_2 supposed to be? Is A supposed to be the matrix that produces those above linear transformations?

Okay the question is to find the Fourier transform of: rect(\frac{x}{5})\otimes(\delta(x+3)-\delta(x-3)) =F^{\infty}_{\infty} \intrect(\frac{x'}{5})(\delta(x+3-x')-\delta(x-3-x')) dx' [1] - where F represents a Fourier transform. My Issue Okay I am fine doing this using the convolution...