Transformation Definition and 1000 Threads

Homework Statement Homework Equations included in the first picture The Attempt at a Solution i feel confident in my answer to part "a". i pretty much just did what the u and v example at the top of the page did. but for part "b" i tried to distribute and collect like terms and what not...

Homework Statement From Hoffman and Kunze: Is there a linear transformation T from R^3 to R^2 such that T(1,-1,1)=(1,0) and T(1,1,1)=(0,1)?Homework Equations T(c\alpha+\beta)=cT(\alpha)+T(\beta) The Attempt at a Solution I don't really understand how to prove that there is a linear...

How do you transform a curvy coordinate system to that in euclidean space? An example will be greatly appreciated.

V′μ=((∂yμ)/(∂xν))*Vν This is a contravariant vector transformation. (Guys I am really sorry for making the formula above looks so incomprehensible as I still new to this.) For the y in the partial derivative, is y a function in terms of x? In that sense, is it formula that maps x to y? Is it...

To prove the wye-delta transformation formula, it is said 'If the two circuits are to be equivalent, the total resistance between any two terminals must be the same.' But why ? I can't convince myself that it is sufficient condition for the equivalence of circuits.

Homework Statement For the balanced three-phase loads shown in FIGURE 3, ZY = (15 + j15) Ω and ZΔ = (45 + j45) Ω. Determine: Uploaded file C1.png (a) the equivalent single Δ-connected load, (b) the equivalent single Y-connected load obtained from the Δ-Y transformation of (a) above, (c) the...

As known, any Lorentz transformation matrix ##\Lambda## must obey the relation ##\Lambda^μ{}_v####\Lambda^ρ{}_σ##gμρ=gvσ . The same holds also for the inverse metric tensor gvσ which has the same components as the metric tensor itself (don't really understand why every tex formula starts from a...

Homework Statement If two particles have velocities u and v in frame S, find their relative speed in frame S'. Homework EquationsThe Attempt at a Solution Isn't it strange that the relative speed doesn't depend on the velocity of the frame, ##\vec s##? Since the two particles have velocities...

Homework Statement Use the Lorentz Transformation equations to derive the formula relating the time period of a moving clock to that of a stationary clock Homework Equations X'=y(X-vt) Y'=Y Z'=Z t'=y(t-vx/c^2) The Attempt at a Solution t'=1/sqrt(1-(v/c)^2) . (t-vx/c^2)

I understand the concepts behind the terms in the title; however, I have a question about how to transform the wave energy itself. I'm working on a science fair project that involves transforming sound energy into electrical energy--I understand this is not a very reasonable method of harvesting...

Hi all,I am trying to understand relativity and Lorentz Transformation more clearly but I have some problems. Assume that we have frame F' which is moving at velocity v with respect to F. Now assume we have an object, O, moving at velocity, w, with respect to F. Frame F has its own time, t, and...

Homework Statement Homework EquationsThe Attempt at a Solution a) the question is to transform star to delta ?

hi, i know unitary transformation - but could not get where do we need finite and infinite unitary transformation ? please help me in this regard. thanks

I'm trying to derive (14.25) in B&J QFT. This is ##U(\epsilon)A^\mu(x)U^{-1}(\epsilon) = A^\mu(x') - \epsilon^{\mu\nu}A_\nu(x') + \frac{\partial \lambda(x',\epsilon)}{\partial x'_\mu}##, where ##\lambda(x',\epsilon)## is an operator gauge function. This is all being done in the radiation...

r\rightarrow r-2qz and \psi\rightarrow\psi+q\cdot(r-qz), I don't know how to derive it, anybody know? This question results from the book "Optical Solitons: From Fibers to Photonic Crystals [1 ed.]" section 6.5

Sorry for such a simple question but where do we model the energy going during phase transitions? If I had a mercury thermometer in a pot of water, and I had a 200 degree Celsius heat reservoir in contact with the water, I would see the water temp hold steady during the phase transition...

Hi everyone, I am having some problems understanding Bergmann's problems. Problem 3 from Chapter 4 from Intro to the Theory of Relativity by Bergmann 1. Suppose that the frequency at a light ray is f with respect to a frame of reference S. Its frequency f′ in another frame of reference, S'...

If we have: $$F_{\mu\nu} \rightarrow \cos\alpha F_{\mu\nu} +\sin\alpha \star G_{\mu\nu}$$ $$G_{\mu\nu} \rightarrow \cos\alpha G_{\mu\nu} +\sin\alpha \star F_{\mu\nu}$$ for rotation $\alpha$. If infinitesimal transformation for small alpha one gets $$\delta F_{\mu\nu} = \delta\alpha~\star...

I should mention that I'm self-studying this material, not taking it as part of a course, but since this is still a homework-style problem I figured it'd be best to post here. Homework Statement In Peskin and Schroeder problem #11.2, they ask us to consider the Lagrangian: $$\mathcal{L} =...

if A is a square matrix, and A' = B-1AB is its similarity transform (with a non-singular similarity transformation matrix B), then the eigenvalues of A and A' are supposed to be the same. I can verify this for all most all cases of A. But, it doesn't seem to work, when the eigen values of A are...

I was reading in this book: Supergravity for Daniel Freedman and was checking the part that has to do with Extremal Reissner Nordstrom Black Hole. He was using killing spinors (that I am very new to). I was understanding the theory until he stated with the calculations: He said that the...

In SR the speed transformation formula (in response to a change of inertial frame of reference) is usually derived from the Lorentz transformation of space and time coordinates. I would like to find a direct derivation starting from the existence of a maximum speed limit (c) in respect to any...

Homework Statement t:P_3 -----> P_3 p(x) |---> p(x) + p(2) Determine whether or not this function is linear transformation or not. Homework Equations For a function to be a linear transformation then t(0) = 0 , there are other axioms that must be satisfied, but that is not the problem...

My local PBS station broadcasts a physics series on a sub-channel. They call it The Mechanical Universe locally. PBS recently broadcast The Lorentz Transformation . It appears that one may view these on line, as the Lorentz Transformation began to load after I allowed it to pop-up. There are...

Hey guys, i did this source transformation as an alternate method to find the transfer function of a circuit, however I am getting a different transfer function of 2/(2s+(s+3)(s^2+1)) to the solution in the following image. Any help would be really appreciated :)

Homework Statement [/B] I'm trying to derive (14.25) in B&J QFT. This is ##U(\epsilon)A^\mu(x)U^{-1}(\epsilon) = A^\mu(x') - \epsilon^{\mu\nu}A_\nu(x') + \frac{\partial \lambda(x',\epsilon)}{\partial x'_\mu}##, where ##\lambda(x',\epsilon)## is an operator gauge function. This is all being...

We have a r.v. X with p.d.f. = sqrt(θ/πx)*exp(-xθ) , x>0 and θ a positive parameter. We are required to show that 2 θX has a x^2 distribution with 1 d.f. and deduce that, if x_1,……,x_n are independent r.v. with this p.d.f., then 2θ∑_(i=1)^n▒x_ι has a chi-squared distribution with n...

Homework Statement let A be the matrix corresponding to the linear transformation from R^3 to R^3 that is rotation of 90 degrees about the x-axis Homework Equations find the matrix A The Attempt at a Solution I got stuck on rotating z component. I tried T([e1,e2,e3])=[0 -1 0]...

Was reading how do vectors transform under chiral transformation and found the following: If $$V^\mu$$ is a vector; set $$ V^\mu = \bar{\psi} \gamma^\mu \psi= $$ $$\bar{\psi}\gamma^\mu e^{-i\alpha\gamma^5}e^{i\alpha\gamma^5}\psi =$$ $$\bar{\psi}\gamma^\mu\psi = V^\mu $$ My questions are why...

Transform the left hand member into the right hand member. $\frac{\tan\alpha+\tan\beta}{\sec\alpha-\sec\beta}=\frac{\sec\alpha+\sec\beta}{\tan\alpha-\tan\beta}$By using cross multiplication I was able to prove this identity but what I actually want to accomplush is to transform the left member...

I already did everything that I can to transform the left side member to the right side member but I always get a jumbled terms. Please give me a hand on this problem. $(2\sin^{2}(\theta)-\cos^{2}(\theta))^{2}-9(2\sin^{2}(\theta)-1)^{2}=(2-3\sin^{2}(\theta))(2+3\sin(\theta))(3\sin(\theta)-2)$

Hey there, I trying to understand the following coordinate transformation of the equation of continuity (spherical coordinates) for a vaporizing liquid droplet\frac{\partial \rho}{\partial t} + \frac{1}{r^2} \frac{\partial}{\partial r} (r^2 \rho v) = 0 into \epsilon \sigma \frac{\partial...

Find the matrix for the transformation that projects each point in R3 (3-D) perpendicularly onto the plane 7x + y + 3z = 0 . The attempt at a solution is attached for question 1 (actually instructor's solution) I kind of understand it but ... why is n <dot> v = equation of the plane? Does v...

Find the matrix for the transformation that projects each point in R3 (3-D) perpendicularly onto the plane 7x + y + 3z = 0 . The attempt at a solution is attached for question 1 (actually instructor's solution) I kind of understand it but ... why is n <dot> v = equation of the plane? Does v...

Hi there, I am reading a material on the application of Fourier transformation in physics. One application is to transform the position-dependent function to k-dependent function, i.e.## F(k) = FFT[f(x)]## We know that the in physics, the wavenumber could be written in momentum as...

Homework Statement Hey guys! So I have a Lagrangian with two coupled fields like so: \mathcal{L} = \frac{1}{2}(\partial_{\mu}\phi_{1})(\partial^{\mu}\phi_{1})...

Homework Statement I'm to use source transformation to find the current through the 24 Ohm resistor 2. The attempt at a solution I used source transformation on the left 12V source and got a .5A current upwards. The 24 and 30 ohm resistor are in parallel so I found an equivalent resistance of...

Homework Statement I am supposed to show that the free Schrödinger Equation is NOT kovariant under Galilei Transformation. Homework Equations We learned in Lectures that the Galilei Transformation can be written as: \vec{x'}=\hat{R}\vec{x}-\vec{a}-\vec{v}t (1) or equivalently...

Homework Statement Suppose two observers O and O', whose positions coincide , each sets up a set of 2D cartesian coordinates (x,y) and (x',y') respectively to describe the position of a certain object at a fixed point . Derive a set of formulae for one observer to convert the other observer's...

Homework Statement I haven't learned kernel yet so if that's of use here I don't know it yet let ##T: \mathbb{R^3} \rightarrow \mathbb{R^2}## where ##T<x,y,z>=<2y,x+y+z>##[/B] prove that the range is ##\mathbb{R^2}## The Attempt at a Solution I know that T is not one-to-one, I checked that...

Homework Statement let ##T:\mathbb{R^3} \rightarrow \mathbb{R^3}## where ##T<x,y,z>=<x-2z,y+z,x+2y>## Is T one-to-one and is the range of T ##\mathbb{R^3}##? The Attempt at a Solution I took the standard matrix A ##\left[\begin{array}{cc}1&0&-2\\0&1&1\\1&2&0\end{array}\right]## det(A)=0 so...

Homework Statement Problem 29. Use the subtraction trick U(tilda) = U−U1 to reduce the following problems with non-canonical boundary conditions to the canonical ones and write down the equations in terms of the variable ˜u (do not solve them). Note that there are infinitely many u1’s that...

Hello, I'm currently going through Agrawal's book 'Nonlinear Fiber Optics' and got stuck with some mathematical cosmetics (pp. 40). It is the substition of: \vec{P_L}(\vec{r},t) = \frac{1}{2} \hat{x} \left(P_L \exp{(-i \omega_0 t)} + c.c.\right) into \vec{P_L}(\vec{r},t) = \epsilon_0...

Homework Statement Let T:R->R^2 be the linear transformation that maps the point (1,2) to (2,3) and the point (-1,2) to (2,-3). Then T maps the point (2,1) to ...Homework Equations T(xa+yb) = xT(a)+yT(b)The Attempt at a Solution Okay so I have the solution to this problem, but its understanding...

Homework Statement There's a person and he ate a hamburger which its 2000 kcal.And he wants to spend this energy . he will be weightlifting and he will lift 45 kg to 2 meters.How many times he can lift it ? Homework Equations W=Fx or W=mgh The Attempt at a Solution 2000...

Apriori -- before taking any of the postulates of special relativity into account -- we might say that the lorentz transformations between two frames K and K', where K' is moving w. speed v along the x-axis of K, is given by $$\vec{x}' = F(\vec x, t)$$ and $$t' = G(\vec x, t).$$ Now, i want...

Hi, First of all, I'm not sure if this thread belongs to the BSM forum because the question I'm posing here is a simple CFT question which could well be posed in the forum on GR or Particle Physics/QFT. I will defer to the judgment of the moderator to put this in the right place if it already...

Not sure if Velocity Addition belongs in introductory Physics but it seems relatively introductory to me. I'm having trouble with all aspects of grasping how to attempt these problems logically. Obviously the math behind them is super simple; I just more or less don't know what to plug in where...

Hello, I was reading and trying to follow up with Pierre Ramond's "Field theory: A modern primer" and got stuck in his step to step jumping. Kindly, see attachment and note that Eq (1.2.6) = g_{ρσ}=g_{μ\upsilon}\Lambda^{μ}_{ρ}\Lambda^{\upsilon}_{σ}. My question is what do I need from tensor...

I'm being asked to derive the velocity transformation between vy and vy' and my result isn't exactly matching my goal but I don't know what I'm doing wrong. It's an introductory modern physics course and we're covering special relativity. Assume a reference frame S' moving in some constant...