Transformations Definition and 823 Threads

Hi,all, I m an undergrades and I am suffering on understanding the different representation transformations, namely from schrodinger picture to interaction picture tupically, my lecturer didn't state which representation he was using and I m so confused, any helps would be great. Shall I bring...

Homework Statement The Attempt at a Solution So I observed: T(B) = λB T-1(B) = λ'B Also, T-1(T(B)) = λ'λB = B This implies, λ'λ = 1 And so, there should be a relation λ = \frac{1}{λ'}. Is that right?

Hi, Two questions: 1) Compute the matrix product corresponding to the composition of the transformations. Let U = P4(R) [polynomial degree 4], V = P3(R) , and W = P2, and let S = d/dx (derivative) and T = d/dx (derivative). Then the composition TS = d^2/dx^2 (second deriv) Attempt...

I want to understand how to make a Mobius Transformation.If someone can help me with an example that will be great. Let's say we have f(0) = i, f(1) = 1, f(−1) = −1 for instance ...how should I proceed in finding one?Thank you

Homework Statement Some matrix transformations f have the property that f(u) = f(v), when u ≠v . That is, the images of different vectors can be the same. For each of the following matrix transformations f : R^{2} → R^{2} defined by f(u) = Au , find two different vectors u and v such...

What is the most tangible way to introduce linear transformations in a linear algebra course? Most books tend to take a very abstract approach to this topic.

I tried to prove that a hermitian matrix remains hermitian under a unitary similarity transformation.I just could do it to he point shown below.Any ideas? [ ( U A U ^ {\dagger}) B ] ^ {\dagger} = B ^ {\dagger} (U A U ^ {\dagger}) ^ {\dagger} = B (U A^ {\dagger} U ^ {\dagger}) thanks

Okay so I've done very well in college so far, and I thought I was at least decent at math, but I just started this precalculus class and I'm having an issue. I basically don't know, and can't get a straight answer about how to handle functions that have multiple transformations going on...

Hi, I hope this is the right forum to post. My question is, which is the math implied for transforming an objectA local space, to anothers objects local space, and then transforming it to world space? For example, Lets say we want to know if objectA is infront of objectB, So the...

Homework Statement http://s2.ipicture.ru/uploads/20120109/dT4m6rNG.jpg The attempt at a solution x=\frac{u}{1+v} and y=\frac{uv}{1+v} Transforming the integrand: \frac{x+y}{x^2}e^{x+y}=\frac{(1+v)^2 e^u}{u} dxdy=J.dudv J=\frac{v(1+v)^2 +1+uv}{(1+v)^3} The double integral becomes: \int\int...

Homework Statement http://s2.ipicture.ru/uploads/20120107/vVVkUT7f.jpg The attempt at a solution I plotted the graph x-y: http://s2.ipicture.ru/uploads/20120107/ja3V9aSV.jpg y=\frac{1}{2}(u+v) and x=\frac{1}{2}(u-v) So, after finding the Jacobian, the double integral becomes: \int\int...

Homework Statement A charge q is released from rest at the origin, in the presence of a uniform electric field and a uniform magnetic field \underline{E} = E_0 \hat{z} and \underline{B} = B_0 \hat{x} in frame S. In another frame S', moving with velocity along the y-axis with respect...

Homework Statement Q is an invertible self-adjoint linear transformation on an inner product space V. Suppose Q is positive definite. I have already shown that inv(Q) is self-adjoint, that all eigenvalues of Q are positive, so there exists S s.t. S^2 = Q. Now suppose P is any self-adjoint...

I was struck with the following question: Is there a linear map that's injective, but not surjective? I know full well the difference between the concepts, but I'll explain why I have this question. Given two finite spaces V and W and a transformation T: V→W represented by a matrix \textbf{A}...

Homework Statement Given the following defined transformation T(a + bt+ct^{2}) = (a+c) - (c+b)t + (a+b+c)t^{2} find the matrix with respect to the standard basis From my understanding, the standard basis for a 3 element vector would be (0,0,1)^{T} (0,1,0)^{T}...

A quasar is moving away from the Earth with a speed of 0.850C. It emits a proton that eventually reaches earth, and is traveling at a speed of 0.519C relative to the earth. How fast is the proton moving relative to the quasar? Is this answer as simple as it seems? is the answer simply...

Homework Statement An excited nucleus of krypton-80 emits a gamma ray that travels at the speed of light relative to the nucleus. The nucleus itself has a speed of 0.60c relative to the sun. Use a relativistic velocity transformation to determine the speed of the gamma ray relative to the...

Hi all, I came up with the following problem myself and am trying to solve myself. I haven't seen it in any txtbook, grad or undergrad. Suppose you have the ground frame (Earth). Earth sees ship1 start at t=0, v=vo1, at x=xo1. Earth sees ship2 start at t=0, v=vo2, at x=xo2 All...

Is it possible, in general, to have a one-to-one transformation from Rn to Rm for n>m? I'm thinking in the context of geometry, where you want to map a bounded region from a higher space to a lower space.

The derivation of the Lorentz transformations is based on the homogeneity[of space and time] and the isotropy of space. Could one derive the same transformations wrt space which is not homogeneous or[not] isotropic? You may consider a few chunks of dielectric strewn here and there. I am...

Homework Statement Space ships A and B, each having a proper length of 100m, pass each other moving in opposite directions. According to the clocks on ship A, the front end of B takes 1.5 x 10^(-6) s to pass the entire length of A. a) what is the relative velocity of the two ships? b)...

For fun, I'm writing a simple special relativity simulator with a much smaller speed of light so that relativistic effects are clear even at low speeds. I already have time dilation and speed of light delay working. However, right now, the speed of light does NOT always appear to be the same for...

Homework Statement Find two linear operators T and U on R^2 such that TU = 0 but UT ≠ 0. The Attempt at a Solution Let T(x1,x2)=(0,x2) Let U(x1,x2)=(x2,0) TU(x1,x2)=T(x2,0)=(0,0) Am I right? 'Cause I can't remember if TU(x1,x2)=T[U(x1,x2)] Or TU(x1,x2)=U[T(x1,x2)]

Homework Statement Given: T is a linear transformation from V -> W and the dim(V) = n and dim(W) = m Prove: If β = {v1, ..., vm} is a basis of V, then { T(v1), ..., T(vm) } spans the image of T. NOTE: because of bad hand writing I can't tell if the bold is suppose to be an 'm' or an 'n'...

Homework Statement Homework Equations NoneThe Attempt at a Solution Well guys, this is a problem I've been having for the last 2 days and with my midterm tomorrow I have no time to fiddle around with it. So, I do not understand how (where it says b) how Im going to use a division symbol ( /...

Hello -- I have some reference object R (e.g. a protein), and I've got two transformations t1 and t2 (e.g. a transformation = quaternion + translation). In my case, t1 and t2 were obtained from symmetry operations. So after applying t1 to R I get object T1, and after applying t2 to R I get...

Homework Statement Show that if { v_1, ... , v_k} spans V then {T(v_1), ... , T(v_k)} spans T(v) Homework Equations The Attempt at a Solution So we know that every vector in V can be written as a linear combination of v_1,...v_k thus we only need to show that {T(v_1)...

Hello, I read somewhere that in 2D, the Möbius transformations do not represent all the possible conformal transformations, while according to Liouville's theorem, in spaces of dimension greater than 2 all the conformal transformation can be expressed as combinations of...

Hi. So if you have \frac{d p_{\alpha}}{ds} = \frac{q}{c} F^{\alpha \beta} u_{\beta} how could you possibly go on proving this its form is invariant under all coordinate transformations? Or any physical law of any form, really? I guess my point is how do you represent "all possible...

Homework Statement Homework Equations The Attempt at a Solution In the previous problem I was asked to identify if a polynomial, such as f(x)=2x was a linear transformation. In that case I checked to see if f(ax + by) = f(ax) + f(by). I figure I would be doing something...

Homework Statement I'm having trouble understanding coordinate transformations for vector fields. There are two 'coordinate pieces', the coordinates pieces of the vector at a point changes, and the function describing the field can also be rewritten in terms of the new coordinates. I'm...

Homework Statement Show that 2.1.1 is equivalent to the totality of 2.1.2 and 2.1.3.Homework Equations The Attempt at a Solution aTx + bTy = aT(x) + bT(y) = T(ax) + T(by) = T(ax + by) ?

Homework Statement Let T:ℝ^{2}→ℝ be defined by T\left(\begin{array}{c} x_{1} \\x_{2}\end{array}\right) = (0 if x_{2} = 0. \frac{x^{3}_{1}}{x^{2}_{2}} otherwise.) Show that T preserves scalar multiplication, i.e T(λx) = λT(x) for all λ \in ℝ and all x \in ℝ^{2} The Attempt at a Solution...

I have seen in various locations different conventions regarding the location of a prime symbol denoting a tensor represented in a new frame. For example, if the position four-vector is x^{\mu} then this four-vector in a different frame is often written as either x'^{\mu} or...

I did the problem but I just need to make sure I did it correctly.. If I did it incorrectly, please let me know. Homework Statement Page 1: http://i55.tinypic.com/25sosgp.jpg (Zoom in) Page 2: http://i52.tinypic.com/ofyds5.jpg (Zoom in) Homework Equations Problem 4 a-d The Attempt at a...

Hi, I'm working through Schutz's intro to GR on my own, and I'm trying to do problems as I go to make sure it sinks in. I've encountered a bump in chapter 5, though. I don't think this is a tough problem at all, I think it's just throwing me off because x and y are coordinates as well as...

Homework Statement Let T: R3 - R3 be the linear operator given by T = -y + z -x + z x + y Find a basis B' for R3 relative to which the matrix for T is diagonal using the standard basis B for R3. Homework Equations [T]B' = P-1[T]BP The Attempt at a Solution...

I am currently doing a course on Computer Graphics Algorithms. This involves lot of matrix transformations i.e. for eg - rotating co-ordinates, translating, reflecting etc. I am solving the problems on paper using a calculator, but I need some software which will help me verify the solution...

Homework Statement Let T: P2 - P2 be the linear operator defined by T(a0 + a1x + a2x2) = a0 + a1(x - 1) + a2(x - 1)2 (a) Find the matrix for T with respect to the standard basis B = {1, x, x2}. Homework Equations [T]B[x]B = [T(x)]B The Attempt at a Solution T(1) = a0 + a1(1 -...

oblique and horiz asymptotes, axis same transformations and other things. i do not understand these at all and the text makes no sense (see attachment). i can find the asymptotes of all types, but i do not understand how the methods i use work. please explain the methods and the reasoning...

Homework Statement Prove that the spacetime interval -(ct)^{2} + x^{2} + y^{2} + z^{2} is invariant. [/itex] Homework Equations Lorentz transformations \Deltax' = \gamma(\Deltax-u\Deltat) \Deltay' = \Deltay \Deltaz' = \Deltaz \Deltat' = \gamma(\Deltat-u\Deltax/c^{2}) The...

Thanks for reading! Homework Statement I have been given a proof for the lorentz transformations (which I only partly understand) that relied on the two relativity postulates (equivalence of inertial systems and the speed of light being constant) for the case of two standard inertial...

In school I've always learned that tensor transformations took the form of: \mathbf{Q'}=\mathbf{M} \times \mathbf{Q} \times \mathbf{M}^T However, in all the recent papers I've been reading. They've been doing the transformation as: \mathbf{Q'}= \frac {\mathbf{M} \times \mathbf{Q}...

I'm slowly trying to understand sp relativity. I admit I got lost in the last thread I posted :blushing:. But thanks to all who replied! I have a question about the Lorentz transformations formulas. This is more of a mathematical question about how the formulas are derived. If you have...

Suppose i release a particle at (x=a,y=0) with (p_x = b, p_y = 0) and you release one in the transformed state (x=0, y=a) with (p_x = b, p_y = 0) where the transformation is that we rotate the coordinates but not the momenta. This is a non canonical transformation that leaves H invariant. Show...

While it's pretty easy to derive the infinitesimal version of the special conformal transformation of the coordinates: x'^{\mu}=x^{\mu}+c_{\nu}(x^{\mu} x^{\nu}-g^{\mu \nu} x^2) with c infinitesimal, how does one integrate it to obtain the finite version transformation...

I've studied classical physics and never heard this before until recently...the allowable coordinate transformations for classical mechanics are rotations and translations. Could someone explain why this is so? What makes these "allowable" (I know they are orthogonal transformations).

Hi, I am confused about a lot of Fourier transformations: A Fourier transform with variable f A Fourier transform with variable e^{jw} Fourier series What is the difference between these different Fouriers? Another thing, when does the convolution in the time domain become a multiplication...

In SRT, Force (F) transforms identically to d(mV)/dt, which can in turn be transformed using the Lorentz transformations and the dependence of m upon speed. This raises the question whether Force in the force laws also transforms the same way among different reference frames. Certainly the...

Many equations are affected by Lorentz transformations. Time, mass, volume of a moving object, momentum, force etc. I want to know if the following equations are affected by Lorentz transformations: 1. Distance=velocity*time (r=vt) 2. E=hv 3. j*=ot 4. F=G*m1*m2/r^2 Also, is the Newton's...