Transformations Definition and 863 Threads

http://img34.imageshack.us/img34/5391/13262160.jpg http://g.imageshack.us/img34/13262160.jpg/1/ http://img46.imageshack.us/img46/7397/62501858.jpg http://g.imageshack.us/img46/62501858.jpg/1/ http://img7.imageshack.us/img7/2651/15142727.jpg...

I need help with calculation of several Laplace transformations. I'm not sure about following word expressions, which I'll use, as english is not my mother tongue, but I hope It will be understandable. 1. Find transformation to this object: f(t) = 3t\sinh^2t - 4\int_{0}^{t}(e^s \cos hs -...

Homework Statement Let P3 be the space of all polynomials (with real coefficients) of degree at most 3. Let D : P3 -> P3 be the linear transformation given by taking the derivative of a polynomial. That is D(a + bx + cx2 + dx3) = b + 2cx + 3dx2: Let B be the standard basis {1; x; x2; x3}...

Homework Statement Show that (D'Alembertian)^2 is invariant under Lorentz Transformation. Homework Equations The book (E/M Griffiths) describes the D'Alembertian as: \square^2=\nabla^2-\frac{1}{c^2}\frac{\partial^2}{\partial t^2} The Attempt at a Solution I don't really...

I thought this problem was pretty straightforward, but I can't seem to match the answers in the back of the book. The problem is: Find the determinant of the following linear transformation. T(v) = <1, 2, 3> x v (where the x means cross product) from the plane V given by x + 2y +...

Homework Statement Let B={b1,b2} be a basis for R2 and let T be the linear transformation R2 to R2 such that T(b1)=2b1+b2 and T(b2)=b2. Find the matrix of T relative to the basis B. The Attempt at a Solution I know that the matrix I'm looking for needs to be 2x2 and that the standard matrix...

I've recently come to the conclusion that i need to learn matrices. I read that matrices correspond to linear transformations and that every linear transformation can be represented by matrices, but what are linear transformation, and how do you represent it by a matrix?

http://img513.imageshack.us/img513/3874/85311748.th.jpg Can someone please ler me know how to go about this problem? I have made z the subject, however do not know how to advance. Thanks

Notations: L(V,W) stands for a linear transformation vector space form vector space V to W. rk(?) stands for the rank of "?". Question: Let τ,σ ∈L(V,W) , show that rk(τ + σ) ≤ rk(τ) + rk(σ). I want to know wether the way I'm thinking is right or not, or there's a better explanation...

Help! What are the P and T transformation laws for the electromagnetic vector potential, A_\mu? and how are these consistent with the transformation laws of the electric and magnetic vectors that I am familiar with? under P: E is odd, B is even under T: E is even, B is odd When I try to...

I'm struggling to grasp what should be a trivial property of singular value decomposition. Say that I have a linear transformation T that is non-singular (i.e. T^{-1} exists) and relates matrices A and B: B = T A or A = T^{-1} B What I would like to know is how the singular values...

Assignment question: Let V = P (R) and for j >= 1 define T_j(f(x)) = f^j (x) where f^j(x) is the jth derivative of f(x). Prove that the set {T_1, T_2,..., T_n } is a linearly independent subset of L(V) for any positive integer n. I have no idea how...

The problem is T(x + yi) = x - yi Show that this is a linear transformation and find the matrix of the transformation using the following basis (1+i, 1-i) ARGH I am having trouble with the complex numbers for some reason! To show that it is linear I have to show T(x + yi...

Homework Statement T: P2 --> P2 be a linear transformation defined by T(p(x)) = xp'(x) where ' is the derivative Describe the kernal and range of T and are any of the following polynomials in the range and or in the kernal of T? 2 x2 1 - x Homework Equations power rule (for...

Homework Statement The matrix \left[ \begin{array}{ccc} 0 &1 &0 \\ 0 &0 &1 \\ 1 &0 &0 \end{array} \right] represents a rotation. (a) Find the equation of the axis of this rotation. (b) What is the angle of the rotation? Homework Equations \left[ \begin{array}{ccc} 1 &0 &0...

Do canonical transformations simply transform the coordinates of a particular system, leaving the physics unchanged? or can they transform between physically different systems? I haven't seen any evidence which shows that they keep the physics the same, but I don't see their usefulness otherwise.

I'm having some difficulty understanding how to perform linear transformations on matrices. I understand the definition but not how to perform the operations. I'm going to give a few examples from my book: Suppose that T: R^2 \longrightarrow R^2 is a linear transformation such that...

In the story below, where would you see possible alternatives, or where would you see a problem? (01) Let us consider a set of physicists {P0, P1, P2, P3, ...} each at rest in their own inertial frames. (02) Let us elect one of them (P0) as the boss to manage an experiment. (03) Let us...

Can anyone explain the above-i've read about in books, internet sites and still do not understand what its doing or the maths. Thanks

Can anyone explain the above-i've read about in books, internet sites and still do not understand what its doing or the maths. Thanks

Hello, In conformal geometry there is a 15-parameter symmetry group. I have an rough conceptual understanding of the 3 spatial translations, the 1 temporal translation, the 3 rotations, the 3 Lorentz "boosts", and the 1 dilation transformation. I am having trouble conceptualizing the...

1. A cosmic-ray proton streaks through the lab with velocity 0.85c at an angle of 50o with the +x direction (in the xy plane of the lab). Compute the magnitude and direction of the proton’s velocity when viewed from frame S’ moving with β=0.72 in the +x direction. 2. Ux'= Ux-v/1-vUx/c^2...

1. Using the Lorentz Transformations, show that the quantity px - Et is invariant, where p and E are the momentum and energy, respectively, of an object at position x at time t. 2. px - Et 3. I needed help on starting the problem. Where should I begin?

Question and solution http://img141.imageshack.us/img141/4881/74319855am1.th.jpg http://img141.imageshack.us/img141/1295/58915812pu1.th.jpg Can someone please explain the solution - why is the right hand matrix t(k-4) t(1+k)? Thanks a lot in advance

1. Suppose V,W are vector spaces over a field F and that T: V ---> W is a linear transformation. Show that for any v belonging to V that T(-v) = -T(v) 2. -T(v) denotes the additive inverse of T(v) 3. I think I'm really overcomplicating it =/ But i have 0v = T( v - v ) = T(v) +...

Hey, not strictly homework but this is probably the best place for it, I wonder if you guys can help me out with a past paper question I've been pondering: Two events occur at the same place in an inertial reference frame S, but are separated in time by 3 seconds. In a different inertial frame...

I'm reviewing for exams and don't understand when to use which Lorentz velocity equation to use. one goes v'=(v-u)/(1-vu/c^2) and the second v=(v'+u)/(1+v'u/c^2)

A = \left[\begin{array}{ccccc} 1 & -1 \\ 2 & 5 \\ 3 & 4 \end{array}\right] Let T_{A}: R^2 \rightarrow R^3 be the matrix transformation that maps a 2 \times 1 column vector x in R2 into the 3 \times 1 column vector Ax in R3. The relationship can be expressed as TA(x) = Ax Find a vector...

Hi, I would like to transform a vector from Spherical to cartesian coordinate system. But the question is probably not that straight forward. :( I have a vector say E = E_r~\hat{r}+E_{\theta}~\hat{\theta}+E_{\phi}~\hat{\phi}. But I know only the cartesian coordinate from where it...

Prtesent the Lorentz transformations as dx=g(dx'+Vdt') dt=g(dx-Vdt) In my oppinion dx and dx' represent proper lengths measured in I and in I', dt and dt' representing coordinate time intervals. Do you aggree. Happy new year to all participamts on the Forum

As I try to understand GR, I find coordinate transformations just about everywhere. My question is simply: What is the reason coordinate transformations play such an important role in GR? Thanks.

Homework Statement Find a basis for V. Let W be a vector space of dimension 4. Let beta = {x1, x2, x3, x4 } be an ordered basis for W. Let V = {T in L(W) | T(x1) + T(x2) = T(x4) } Homework Equations L(W) is the set of linear transformations from W to W The Attempt at a Solution...

Homework Statement Determine whether the subset W of the vector space V is a subspace of V. Let V = L(Q4) (the set of linear transformations from rational numbers with 4 coordinates to rational numbers with 4 coordinates). Let W = { T in V = L(Q4) | { (1,0,1,0) , (0,1,0,-1) } is contained in...

Homework Statement Hi all, we just started doing linear transformations in class and I still don't fully understand them. Here's one question I've been stuck on: Let P2(x,y) be the vector space of polynomials in the variables x and y of degree at most 2. Recall the monomial basis for this...

Separating a fraction I don't remember what this method is named in English, but I want to write the fraction \frac{1}{(s^2 + 1)(s-3)(s+2)} in the form \frac{A}{s^2 + 1} + \frac{B}{s-3} + \frac{C}{s+2} I multiply A with (s-3)(s+2), B with (s^2 + 1)(s+2) and C with (s^2 + 1)(s-3)...

I was reading a statistics book, and part of the problem reduces to the calculus problem of doing the following: 1) Let u=x/y, v=y, with domain 0<x<y<1, how to find the ranges of u and v after the transformation? 2) Let u=x/(x+y), v=x+y with domain x>1, y>1, what values can u and v take...

hi all , i need some help concerning the expressions for lorentz transformation of the acceleration. i couldn't derive them?. thanks. :cry:

Homework Statement Prove that an orthogonal transformation T in Rm has 1 as an eigenvalue if the determinant of T equals 1 and m is odd. What can you say if m is even? The attempt at a solution I know that I can write Rm as the direct sum of irreducible invariant subspaces W1, W2, ..., Ws...

Homework Statement Solve the following problems using Laplace Transforms: y' - y = 2e^t, y_0 = 3 y'' + 4y' + 4y = e^{-2t}, y_0 = 0, y_0' = 4 y'' + y = sin(t), y_0 = 1, y_0' = 0 y'' + y = sin(t), y_0 = 1, y_0' = -\frac{1}{2} Homework Equations N/A The Attempt at...

Homework Statement How do I know if this linear transformation is invertible or not? T: [ x ] ---> [ 2y ] [ y ] [ x-3y ] (I also uploaded a small .bmp file to represent this if this looks too ugly) The Attempt at a Solution Well, I thought maybe it could be...

Can a triangle be smoothly transformed to a circle?

Edwards, Tangherlini, Selleri propose synchrony parameter dependent transformation equations we have discussed here. Call them direct transformations. They also their inverse version. As I see they are not used. Is there a special reason for that. Are they of interest? Thanks

If I have a product like [tex] \bar\ psi\gamma^\mu\psi\bar\psi\gamma_\mu\psi [tex] how can i rearrange with Fierz transformations?

Homework Statement Events A and B are simultaneous in frame F and are 18 km apart on a line that defines the x-axis. A series of spaceships all pass at the same speed in the + x-direction, and they have synchronized their clocks so that together they make up a moving frame F'. They time...

I'm trying to transform some functions. These two I haven't succeeded transforming: f(t) = cos((omega)t + tetha) f(t) = sint*cost Also, I need help to find the inverse transform of this function: F(s) = 8 / (s^2 + 4s)

Please, help me! Suppose n is a positive integer and T is in F^n is defined by T(z_1, z_2, ... , z_n) = (z_1+ ... +z_n, z_1+ ... +z_n, ...,z_1+ ... +z_n) Determine all eigenvalues and eigenvectors of T. Thank you in advance!

Homework Statement Hi all. I have the following Fourier transformation: u(x,t) = \sqrt {\frac{2}{\pi }} \int_0^\infty {\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}} \over f} _s (\omega )\,e^{ - c^2 \omega ^2 t} \sin \omega x\,d\omega }, where fs is the...

Homework Statement A ship is moving at 0.45c with respect to earth, and a beacon is fired perpendicular to the ship at 0.65c with respect to the ship. Find the velocity of the beacon with respect to earth. Homework Equations The Attempt at a Solution My main problem here is...

Hi, I am an inorganic chemist and I am looking for some guidance on where to find a mathematical/physical description of phenomena which I have been observing in a solid-state transformation. I am working with a crystalline oxide (MoO3) which I expose to elevated temperatures (750C) in a...

Why the Galileo transformations are not correct for inertial systems which are traveling close to the speed of light? What made Lorentz to correct this?