Transformation Definition and 1000 Threads

Homework Statement Let T:V→V be a linear operator on a vector space V over C: (a) Give an example of an operator T:C^2→C^2 such that R(T)∩N(T)={0} but T is not a projection (b) Find a formula for a linear operator T:C^3→C^3 over C such that T is a projection with R(T)=span{(1,1,1)} and...

http://t.co/XkVpUrtuAA BTW, how to insert a photo url to show an image here at Physics Forum? http://www.dumpt.com/img/viewer.php?file=yfxl69kwf7oisplu6gzw.jpg

I want to try this bilinear transformation of a rectangle to a quad described here http://www.fmwconcepts.com/imagemagick/bilinearwarp/FourCornerImageWarp2.pdf on page 4. I have the square (500,900)(599,900)(599,999)(500,999) and the quad (454,945)(558,951)(598,999)(499,999) It looks like...

Hello, I'm reading Tong's lecture notes on QFT and I'm stuck on the following problem, found on p.11-12. A scalar field \phi , under a Lorentz transformation, x \to \Lambda x , transforms as \phi(x) \to \phi'(x) = \phi(\Lambda^{-1} x) and the derivative of the scalar field transforms...

Homework Statement Find the bilinear transformation that maps the points z1=infinity, z2=i, z3=0 to the points w1=0, w2=i, w3=infinity. Homework Equations w=(az+b)/(cz+d) The answer is -1/z The Attempt at a Solution We have: infinity --> 0 i --> i 0 --> infinity Since 0 goes to infinity...

When one considers a Lorentz transformation between two frames ##S## and ##S'##, such that the coordinates in ##S## are given by ##x^{\mu}## and the coordinates in ##S'## are given by ##x'^{\mu}##, with the two related by x'^{\mu}=\Lambda^{\mu}_{\;\;\nu}x^{\nu} then a scalar field ##\phi (x)##...

Homework Statement [/B] Find a 2 x 2 matrix that maps e1 to –e2 and e2 to e1+3e2Homework Equations [/B] See the above notesThe Attempt at a Solution [/B] I am making a pig's ear out of this one. I think I can get e1 to –e2 3 -1 1 -3 but as far as getting it to reconcile a matrix like...

Hello, a derivation of the lorentz transformation for an arbitrary direction of the relative velocity often makes use of writing the spatial position vector of an event as the sum of its component parallel and perpendicular to the velocity vector in one inertial frame and then transforming both...

Hi, I'm writting a program in the computer and I've to perform a fast Fourier transform to get the frequency domain information. I've read different website, I've watched some videos, etc and I don't fully understand the whole theory about FFT. I've to say that I don't have a solid mathematics...

When proofing the poisson brackets algebraically, what is the tool of choice. Can one use the muti dimensionale chain rule or how is it usally done?

Homework Statement What is the maximum mass of lead you could melt with 2000 J of heat, starting from 25 ∘C ? Lead melts at 328∘C , its specific heat is 128 J/(kg⋅K) , and its heat of fusion is 2.5×10^4 J/kg . Homework Equations Need to find both the mass in the heat of transformation (Q =...

Warning...this requires scripting and iteration, and is not theoretical -- it is a real problem I haven't been able to solve, but I'm sure someone here can... :-) Data: each .csv file is a test recorded at a time interval of 7.5Hz and each file has 3 columns. The first column is time in...

This is problem 11.15 of Jackson, Classical Electrodynamics In a certain reference frame a static, uniform, electric field Eo is parallel to the x axis, and a static, uniform, magnetic induction Bo = 2Eo lies in the xy plane, making an angle theta with the axis. Determine the relative velocity...

Homework Statement Consider ##\mathscr{H} = \frac12 p^2 + \frac12 x^2, ## which is invariant under infinitesimal rotations in phase space ( the ##x-p## plane). Find the generator of this transformation (after verifying that it is canonical). Homework EquationsThe Attempt at a Solution So the...

Homework Statement So we have infinitesimal transformations from ##q_i## to ##\bar{q_i}## and ##p_i## to ##\bar{p_i}## ( where ##p_i## represents the canonical momentum conjugate of ##q_i##) given by $$\bar{q_i} = q_i + \epsilon \frac{\partial g}{\partial p_i}$$ $$\bar{p_i} = p_i - \epsilon...

I'm extreeeeamly rusty at basic circuit theory. I want to transform a sort of infinite arrangement of this circuit: The values themselves aren't important, just the representation of what's happening, all the verticle resistors are the same value as each other, and all the horizontal resistors...

Hello, I'm running a galaxy formation simulation. The output specifies the coordinates in (x, y, z) of all the particles in a galaxy, which usually fall in a disk. The orientation of the disk depends on the initial conditions, but it is generally not aligned with any of the coordinate axes...

Hey everyone! It's my first semester with quantum mechanics and I'm uncertain if my solution of this problem is correct, would be nice if someone could check and let me know :smile: 1. Homework Statement I have to calculate the representation of the state: |\alpha \rangle \equiv exp[-i...

I would like to obtain the conformal map from a uniform rectilinear fluid flowing in the x-direction, where the field is bounded below by the x-axis, to the flow in the w-plane. In the w-plane the flow is correspondingly bounded from below by a trochoid. (A trochoid is a continuous waveform...

Dear PF Forum, First, I'd like to thanks this forum for helping this much and so far. I have a question about Lorentz Transformation. Lots of questions actually :smile: http://en.wikipedia.org/wiki/Lorentz_transformation#Boost_in_the_x-direction Instead of using t and x, I'd like to use ta and...

Homework Statement Find the two numerical values of λ such that \left(\begin{array}{cc}4&3\\1&2\end{array}\right) \left(\begin{array}{cc}u\\1\end{array}\right) =λ \left(\begin{array}{cc}u\\1\end{array}\right) Hence or otherwise find the equations of the two lines through the origin which...

Homework Statement Light (plane wave) reflects from the mirror moving along X-axis with speed V. The wave is orthogonal to the mirror (φ=0°). Write the law for frequency change. Homework Equations I know Lorenz transformation for frequency. The Attempt at a Solution All I do not know is how to...

Homework Statement Describe the transformation in : y=e6x-2 - 4 y=6ex-2 - 4 ? Homework Equations --- The Attempt at a Solution 1)So 6x means stretch parallel to x-axis at s.f of 1/6 and then translation of ( +2 , -4 ) 2) the same but the stretch is parallel to y-axis at s.f of 6 but...

Hello, I have some mathematics background but little to no physics background. I am very interested in physics and am beginning to learn about relativity. Upon exploring the derivation of the Lorentz Transformation equation I noticed something that confused me a little. Again, I don't have much...

1- Let the linear operator on R^2 have the following matrix:A = 1 0 -1 3 What is the area of the figure that results from applying this transformation to the unit square? 2- I am abit confused here, I thought that the matrix for the unit square would be, 0 0 1 0 0 1 1 1... But...

hi guys :D im having trouble with this proof, any hints? let V be a vector space over a field F and let T1, T2: V--->V be linear transformations prove that

Hello, I am having a bit of trouble with calculating the Fourier transformation of a harmonic load. I have the function f(t) = A * sin(ωt) in the time-domain. I would like to represent this function in the frequency domain. What would be its amplitude? Thank you

Pre-knowledge A matrix is a linear transformation if, T(u+v)= T(u) +T(v) and T(cu)=cT(u). Theorem 8.4.2 If V is a finnite dimensional vector space, and T: V-> V is a linear operator then the following are equivalent. a) T is one to one, b) ker(T)=0, c)...

This is a soft question but I think it's a real fact.The Frequency domain has made revolution in the field of Mathematics,Physics,Digital Signal and image Processing etc. Some of concepts which are very difficult to analyse in spatial or time domain can be very easily understood in the frequency...

Homework Statement Show how a Legendre transformation is used to obtain the Helmholtz free energy A(T,V) from the internal energy and derive the general expression for the differential of A. Homework Equations Internal Energy is a function of Entropy and Volume. U Ξ (S, V) A Ξ (T,V) A = U...

http://math.sfsu.edu/federico/Clase/Math350.S15/linea.JPG 1. Homework Statement The picture below represents the map from a "green projective line" to a "red projective line." It takes the "green points" 1,3,7,-11 to the "red points" 0,6,10,20, respectively as shown by the ruler. Let f be the...

Introducing the Hubbard Stratonovich transformation my book uses an expression for completeness that I don't understand (the one indicated on the picture). Can anyone explain why this is indeed unity?

1. Question. A 15 kg child slides from rest, down a playground slide that is 4.0m long. The slide makes a 40degree angle with the horizontal. The child's speed at the bottom is 3.2 m/s. What was the force that the slide was exerting on the child? Answer: 75 N [up the slide] 2. My Attempt. Ek...

t' = γ(t - vx/c2) where t is the time in the stationary frame t' is the time in the moving frame v is the relative velocity between the two frames and x is the distance traveled in the time t in the stationary frame. ∴ x = vt substituting this into the Lorentz time equation gives us: t' = γt(1 -...

Gauge transformation can be written as: ##\psi(\vec{r},t)\rightarrow e^{-i \frac{e}{\hbar c}f(\vec{r},t)}\psi(\vec{r},t)## http://quantummechanics.ucsd.edu/ph130a/130_notes/node296.html Does it have any sense that we choose such function ##f##, that all right side is constant in time. Is this...

Homework Statement You have a unknown Transformation machine T. that transforms from R^4 --> R^3 Vectors U and V are known and the output from T is also known. Can You calculate the values of T? Homework Equations [/B] What values/information is needed to calcuate T ?The Attempt at a...

Hi All, I am trying to understand the directional independence of LT. In contrast, we all know that Doppler Effect is dependent on the direction of motion. I have tried to find any reasoning or explanation and could not find one so far. May be I did not use correct terms in my searches. If...

Hi I began to study the basics of QED. Now I am studying Lagrangian and Hamiltonian densities of Dirac Equation. I'll call them L density and H density for convenience :)Anyway, the derivation of the H density from L density using Legendre transformation confuses me :( I thought because...

Why is ##\bar{\psi}=e^{i\theta}\psi##, where ##\theta## is a real number, used as the global gauge transformation? Why ##e^{i \theta}##; what's the physical significance or benefit? Why is ##\bar{\psi} = e^{i \theta(x)} \psi## the local gauge transformation? What does ##\theta## being a...

Homework Statement Solve the following: $$\mathscr{L}_s^{-1} \left\{ \frac{s}{s^2-s+\frac{17}{4}} \right\}$$ Homework Equations Table of Laplace Transforms.The Attempt at a Solution The solution is $$f(t) = (1/4 )e^{t/2} (\sin(2 t)+4 \cos(2 t))$$ I know I need to break up ##F(s)## into...

Homework Statement The following is Exercise 2.1 from from Ray d'Inverno's 'Introducing Einstein's Relativity.' (a) Write down the Galilean transformation from observer ##S## to observer ##S'##, where ##S'## has velocity ##v_1## relative to ##S##. (b) Find the transformation from ##S'## to...

Trying to answer the question: x"+3x'+2x=u(t-1)+2(t-2)u(t-2), x(0)=1, x'(0)=-1 My book has the answer but I need to see how to solve a problem like this. Professor didn't have time to cover this section but he said one of these might be on the test. Any help is greatly appreciated.

X ={(x1,x2,x2 −x1,3x2):x1,x2 ∈R} f(x1,x2,x2 −x1,3x2)=(x1,x1,0,3x1) 1. Find a basis for X. 2. Find dim X. 3. Find ker f and I am f 4. Find bases for ker f and I am f 5. Is f a bijection? Why? 6. Find a diagonal matrix for f. My attempt: 1. (1, 1, 0, 3) and (1, 2, 1, 6) 2. Dim X = 2 3. Ker f = 0...

Homework Statement I have a body which is instantiated on Earth at some latitude, longitude and altitude. The body has acceleration which is expressed in body coordinates and the acceleration can be integrated to obtain the velocity vector which is also expressed in body coordinates. ECI and...

Can one apply the Hubbard-Stratonovich transformation to the exponential of the Laplace–Beltrami operator?

It's well known when if we are working on problems related to particles in presence of an electromanetic field, the way we state the problem can be done using the next Hamiltonian: H=\dfrac{(p-\frac{e}{c}A)^2}{2m} +e \phi where the only condition for A is: \vec{\nabla } \times \vec{A} =\vec{B}...

When one substitutes the angle -23.7 into the plane stress transformation equation for SigmaX' you indeed get -46.42 MPa (as shown in the images). However, if you substitute this same angle into the plane stress transformation equation for SigmaY', you yield the other principal stress of 116.4...

I just have a quick question on which order around the numerator and denominator should be in the jacobian matrix that multiplies the expression. As in general Lecture Notes on General Relativity by Sean M. Carroll, 1997 he has the law as ## \xi_{\mu'_{1}\mu'_{2}...\mu'_{n}}=|\frac{\partial...

Let S be the frame where the Sun is at rest. Imagine light from the North Star reaches the centre of the Sun, and let's define the equatorial plane as the plane that is perpendicular to this light and cuts the Sun into two hemisphere. Suppose a distant star A is on this equatorial plane and its...

I want to prove that the transformation equation for electric field holds, namely Ex = Ex', where Ex is the x component of E field in S frame and Ex' is that in S' frame, for the special case in which the charged particle has a vertical velocity Uy' in the S' frame (Ux' = Uz' = 0). It is already...