Transformations Definition and 863 Threads

Homework Statement Two flashes of light strike at the same time, at the two orange circles on the diagram. The green train is traveling at a constant 150 kmh relative to the grey platform. The train is 1 km long. As measured by someone at point F on the grey platform, how much time passes...

Homework Statement Let V be a subset of R2 and some fixed 1-dimensional subspace of R2. F:R2->R2 by F(v) = v if v is in V, 0 otherwise Prove that F is not a linear transformation. Homework Equations The Attempt at a Solution Just wondering if i got it right, i don't want to...

Homework Statement Two spaceships approach each other, each moving with the same speed as measured by an observer on the Earth. If their relative speed is 0.70c, what is the speed of each spaceship? My current understanding of the problem. S= wrt observer on Earth S'=wrt one of the...

Homework Statement Hi all - I've been battering away at this for an hour or so, and was hoping someone else could lend a hand! Q: Show that any Mobius transformation T not equal to 1 on \mathbb{C}_{\infinity} has 1 or 2 fixed points. (Done) Show that the Mobius transformation corresponding...

If someone could explain to me how to Transform Circles ? i know how to cransform curves and such. for example there is a question asking me to transform a circle with Origin (57,8.5),r: 0.5 to a circle with orgin (57,8.5) r:6 and anther type which asks me to transform circle with orgin...

Homework Statement The origin (0,0) is in the upper left corner of the image. +x axis goes to the right while +y axis goes down. The artist draws a line from the pixel location (10,20) to the location (210,200) . She wishes to draw a second line that starts at (10,20), is 270 pixels long, and...

Hi, I was given the following problem, and i couldn't solve it yet: Give a bijection between the elements of SO(3) and the fractional linear transformations of the form \varphi_{z,w}\,(u)=\frac{zu+w}{-\bar wu+\bar z}, where u\in \mathbb C\cup \{\infty\};\, z,w\in \mathbb C. Any ideas...

Since the lorentz transformations do not change an object in the z and y directions, but it does in the x direction, is this why a ruler looks shorter in the space station example? (same everything on each station, one moving by your IFR) Also is it why the clock appears to be running slower...

Hi, I have two points on a one-dimensional Euclidean submanifold, say the x-axis. I want to assume that this subspace is kind of "cyclic". This is often accomplished with the compactification R\cup \{ \infty \} The question is: How can I compute distances (up to some constant factor)...

Hey, I have two separate questions: 1) If one is moving in a car and throws a ball straight up, say out the sun roof, the ball will have zero velocity relative to an observer in the car. Conversely, it will have the velocity of the car to a stationary observer. How does one account for drag...

I've tried several hours to understand Lorentz transformations(for space and for time)...it simply dosn't make any sense...I've posted here,on math section,because I need a better mathematical view over it... whitout this I can not understand much out of the restricted theory of relativity,thus...

dear all,we know that active transformation refers to action of changing vectors keeping the operators unchanged whereas passive transformation refers to change of operator components keeping vectors unchanged. what i cannot understand(i am just starting quantum mechanics)is in the former if we...

Homework Statement (124) If a linear transformation T : R3 -> R5 is one-to-one, then (a) Its rank is five and its nullity is two. (b) Its rank and nullity can be any pair of non-negative numbers that add up to five. (c) Its rank is three and its nullity is two. (d) Its rank is two and...

Hi there. This isn't so much a math question as it is a conceptual question. I can't seem to wrap my head around the need for coordinate transformations. *Why* do they need to be done? I think I really need a picture for this, so this might not be the right place to ask, but if you can...

Hi I have a question regarding unitary operators: If an infinitesimal operation (such as a rotation) is unitary does this guarantee that a finite transformation will also be unitary? thanks M

Homework Statement Question 3b from the following file: http://phstudy.technion.ac.il/~wn114101/hw/wn2010_hw07.pdf I know I need to find a generating function for this spacific transformation. but I don't know how to find it, I mean , how I find a spacific transformation for a spacific...

Laplace Transformations... help me please? 1. Homework Statement . Find the laplace transformations of the following: a. \sin\, {\sqrt\,{x}} b. \frac{\cos\,{\sqrt{x}}}{{\sqrt{x}}} c. \ erf\,{(t)}^\frac{1}{2}} d. \int_{t}^\infty\;\frac{\cos\,x}{x}\ e...

Homework Statement Two questions; 1. Let v1 = [-3, -4] and v2 = [-2, -3] Let T: R^2 -> R^2 be the linear transformation satisfying T(v1) = [29, -35] and T(v2) = [22, -26] Find the image of the arbitrary vector [x, y] T[x,y] = [ _ , _ ] 2. The cross product of two vectors in...

Homework Statement Problem 9.7(a) of Goldstein, 3rd edition: If each of the four types of generating functions exists for a given canonical transformation, use the Legendre transformations to derive the relations between them. Homework Equations F = F1(q,Q,t) p = partial(F1)/partial(q) P =...

Let phi(u,v)=(u-2v,-v) is this a R^2->R^2 a linear transformation? I know that there must be two rules that must be met in order to be a linear transformation, after doing the first part, it seems that it may be linear. But I do not know how to show whether or not the second rule is...

In Chapter 1 of Blandford & Thorne: Applications of Classical Physics, section 1.7.1, "Euclidean 3-space: Orthogonal Transformations" (Version 0801.1.K), do equations 1.43 at the beginning of the section, representing respectively the expansion of the old basis vectors in the new basis, and the...

this is a problem confusing me, which is in the book named Principles of Quantum Mechanics by R. Shankar. This problem is not about quantum mechanics, but just in the chapter of Review of Classical Mechanics. (The ******** is just to avoid to be deleted). The problem is in the attachment...

Couple days ago, we get a lecture in relativity, I read quite a lot about it before so there was nothing new except one thing : our professor first started to conclude Lorentz transformation totally in a mathematical way by assuming gamma*(x-v*t) … (what I discovered that it is a known method...

Homework Statement Is the function which rotates the xy-plane by 20 degrees is a linear transformation? From R2 -> R2 Homework Equations x` = xcos\theta + ysin\theta y` = -xsin\theta + ycos\theta Where \theta = 20 degrees (or \pi/9 ) The Attempt at a Solution Apparently...

Here is what the graph looks like on a graphing calculator (notice the equation at the top): http://img62.imageshack.us/img62/8898/graphingcalc.jpg Here is what my graph looks like: http://img53.imageshack.us/img53/7475/lastscanc.jpg I don't understand why the asymptote is...

Homework Statement (1) A1(2,1) --> B1(3,0) A2(0,1) --> B2(3,-2) A3(3,3) --> B3(5,1) P(4,4) The reflection, M, Maps Triangle A onto Triangle B Given that M(P) = Q, write down the coordinates of Q. C1(-3,4) C2(-3,2) C3(-5,5) The rotation R maps Triangle A onto Triangle C...

1. Question: Which of the following linear transformations T from |R^3 to |R^3 are invertible? Find The inverse if it exists. a. Reflection about a plane b. Orthogonal projection onto a plane c. Scaling by a factor of 5 d. Rotation about an axis Homework Equations The Attempt at a Solution...

Hey guys, I was wondering how you would go about proving that the image of a transformation T, im(T), is invariant? And following that, how would you prove T(W1 \bigcap W2) is invariant if T(W1) and T(W2) are both invariant. On an unrelated note, another questions asks to show that TX =...

Homework Statement Let T:U \rightarrow V be a linear transformation, and let U be finite-dimensional. Prove that if dim(U) > dim(V), then Range(T) = V is not possible. Homework Equations dim(U) = rank(T) + nullity(T) The Attempt at a Solution I almost think there must be a typo in the book...

Homework Statement Suppose T is a rotation by 30 degrees about the point 2, and S is a rotation by 45 degrees about the point 4. What is T composed with S? Can you describe this transformation geometrically? Homework Equations none The Attempt at a Solution I know T composed with S...

Hi all. I have here a reference with a representation of the Lie algebra of my symmetry group in terms the fields in my Lagrangian. In order to calculate Noether currents, I would like to use this representation to derive formulae for the infinitesimal forms of the symmetry transformations...

Homework Statement On a supermarket parking lot, a car is pulling out and bumping into an oncoming car. The car pulls out with 0.8 m/s, while the oncoming car has a speed of 1.2 m/s. The angle between the velocities is 24 degrees, as indicated in the figure. What is the collision speed...

Homework Statement The velocity of a ball in an x-y coordinate system is (10, -5) where distance is measured in metres. A second coordinate system, p-q, uses units of feet (1 ft = 0.3048 m). The p-axis is oriented at alpha = 15 degrees relative to the x-axis. The origin of the p-q system is...

Problem: Applied Partial Differential Equations (Richard Heberman) 4ed. #12.3.6 Consider the three dimensional wave equation \partial^{2}u/\partial t^2 = c^2\nabla^2 u Assume the solution is spherically symetric, so that \nabla^2 u =...

Homework Statement f(x) = 5 - g(x) Do you reflect first, then translate, or translate then reflect? Homework Equations The Attempt at a Solution So the graph would be translated up 5 units and reflected over the x-axis. Do you translate it up 5 units, then reflect? or vice versa?

Homework Statement I need to prove this formula, but I'm not sure how to prove it.[T]C = P(C<-B).[T]B.P(C<-B)-1 whereby B and C are bases in finite dimensional vector space V, and T is a linear transformation. Your help is greatly appreciated! Homework Equations T(x)=Ax [x]C=P(C<-B)[x]B...

Hi all, I've taken a two-course undergrad QM sequence and have been reading Shankar's Principles of Quantum Mechanics. There is some reference to the similarity between the Poisson bracket in Hamiltonian mechanics and the commutator in QM. E.g. \{x, p\} = 1 (PB) [x, p] = i \hbar...

Hi I am trying to do a math assignment and I am finding it really difficult. Assume you have a linear transformation from T: P3(R) --> R4 What relevance is there to applying the transformation to the basis elements of P3(R), ie: T(1), T(x), T(x^2), T(x^3)? Why is this subset special...

Homework Statement I'm not sure if this belongs in this section or in one of the physics homework sections. If it has been misposted please move it to the proper area. According to the Theory of Relativity, if an event occurs at a space-time point (x,t) according to an observer, another...

Homework Statement The sine wave sin(t) will only drive the harmonic oscillator y'' + \omega ^2 y into resonance when \omega = 1 . For what values of \omega will the half- and full-wave rectified sine waves drive the harmonic oscillator into resonance. Homework Equations The...

Can anyone explain why it's important to be able to take vectors in an x,y,z coordinate system and be able to transform them into other coordinate systems. Could not all vector considerations be grappled with in the standard x,y,z coordinate systems? How important is this ability to physicists...

I have read that "any" function of new and old coordinates may be used to generate a canonical transformation. However, it seems there must be some restriction on the generating function. For example, if you try to define a generating function for a system with 2 degrees of freedom...

I'm trying to work out how to use the Lorentz equations but so far I haven't been very successful. It would help if I had an example to let me know what I'm aiming for, so if someone would be kind enough to answer my questions about the fairly simple scenario below I would be very grateful...

Hello.The way the transformation of coordenates in Special Relativity are ussually derived presuposes linearity or try do demostrate such linearity using wrong arguments. For example some authors state that since linear and uniform motion remains linear and uniform after the transformation this...

Homework Statement Let T:P[SUB]2 -> P[SUB]2 be the linear operator by T(a[SUB]0 +a1x + a[SUB]2x = a[SUB]o + a[SUB]1 (x - 1) + a[SUB]2 (x-1)[SUP]2 Homework Equations part a ask to find the matrix [T]B - did, see below part b ask to verify matrix [T]B satisfies every vector for [T]B [X]B...

What's the problem with using dimensional analysis to derive the Lorentz transformations?

Homework Statement Let V be a finite dimensional vector space over the field F and let S and T be linear operators on V. We ask: When do there exist ordered bases B and B' for V such that [S]B = [T]B'? Prove that such bases exist only if there is an invertible linear operator U on V such that T...

I am studying invariance, and I came across this dilemma. Suppose we have a subspace with the basis <v1, v2> of the subspace (lets say U2) and we were to map v=c1v1+c2v2 and we let c2=0. Now c1T(v1)+c2T(v2)=k1c1v1+0*T(v2)= k1c1v1. I am doing a proof and need to know what the question means by...

Homework Statement In R3: T1 symmetry with respect to x -√3y = 0 & z = 0 T2 symmetry with respect to the X axis Find: The matrices for T1 and T2, T1(T2) and check that T1(T2) is a rotation around a line.Homework EquationsThe Attempt at a Solution T2 is: \begin{pmatrix} {1}&{0}&{0}&{0}\\...

Homework Statement If f(x)=\frac{2x+1}{x+2}, the equation for y=f^-1(x) is? So I switch x, x=\frac{2y+1}{y+2} The Attempt at a Solution I've tried many ways, but I must be going wrong somewhere, here's what I think to be my nearest: x(y+2)=2y+1 x(y)+2x=2y+1 x(y)+2x-2x=2y+1-2x...