Transformations Definition and 823 Threads

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?

Homework Statement T: R^2-->R2 first rotates points through -3pi/4 radian clockwise and then reflects points through the horizontal x1-axis. Find the standard matrix of T. Homework Equations - The Attempt at a Solution Vector 1 is: (-1sqrt2 - 1 sqrt2) before the reflection, and...

Homework Statement for L, M: V -> W, L, M, linear let||L|| = sup{|L(v)|: v in V, |v| <= 1} show ||L + M|| < ||L|| + ||M|| Homework Equations The Attempt at a Solution so is it true that if |L(x) + M(x)| defines a sup for L + M (x for which |L(x) + M(x)| is the sup), then it also defines a...

Homework Statement Let V be the vector space of all functions f: R->R which can be differentiated arbitrarily many times. a)Let T:V->V be the linear transformation defined by T(f) = f'. Find the (real) eigenvalues and eigenvectors of T. More precisely, for each real eigenvalue describe the...

What is the common name for norm-preserving linear transformations in a normed linear space? I want to say they are the unitary transformations, but I'm just fuzzy enough not to know a good way of proving it.

i need some help with this question - lets say if A = |val1 val2 | |val3 1 | what would AA^t equal? and AA^t and A^T.T are symmetrical. is this true for any 2x2 matrix? thanks in advance

Homework Statement A linear transformation L : R2 -> R3 is defined by: L({\bf{x}}) = \left( {x_2 ,x_1 + x_2 ,x_1 - x_2 } \right)^T I wish to find the matrix representation of L with respect to the orderes bases [u1, u2] and [b1, b2, b3], where u1 = (1,2) u2 = (3,1) andb1 = (1,0,0) b2 =...

Homework Statement It is often stated that many forms of transport transform chemical energy into kinetic energy. Explain why a cyclist traveling at constant speed is not making this transformation. Explain what transformations of energy are taking place. The Attempt at a Solution 1...

Homework Statement T:{R^3 \rightarrow {R^2} given by T(v_1,v_2,v_3) = (v_3 -v_1, v_3 - v_2) If linear, specify the range of T and kernel T The attempt at a solution Okay, I went ahead and tried to find the kernel of T like here: \begin{align*}&v_3 - v_1 = 0\\ &v_3 - v_2 =...

[SOLVED] Linear transformations Homework Statement Determine whether the following maps are linear transformations. (proofs or counterexamples required) a.) L: R^2\rightarrowR^2, (x1) (x2) \mapsto (2x1 + 3x2) (0) The brackets should be two large brackets surrounding the two...

Sorry to bring up again a question that I asked before but I am still confused about this. In SR we have Lorentz invariance. Now we go to GR and one says that the theory is invariant under general coordinate transformations (GCTs). But, as far as I understand, this is simply stating that...

I'm trying to implement AES as practice for my C++ skills, but I've come across a confusing problem that I think belongs here rather than in programming. Rijndael's finite field is GF(28), with reducing polynomial x8+x4+x3+x+1 There is a step in the algorithm that takes a polynomial...

Hi, New here...Can't seem to do latex on here so this post is incomplete until I can work it out. This is maybe quite abstract and generic, but here goes. This problem has niggled me for a while and I need some input please. I have an action S=\int d^4 x \sqrt(g(x))\overline\Phi...

Hello all. I asked this question as a sub-question in another thread where it was perhaps inappropriate. It is very basic but the more i try to understand relativity the nearer to the absolute basics i need to go. The more i learn the less i seem to actually understand. When length and...

Homework Statement Masses of 350g and 175g are attached by a light string and hanging straight down from a light frictionless pulley. The 350g mass is 1.5m above the ground. What speed will the system have when the 350g mass hits the ground. My attempt at a data list is (after i drew a...

I find in the literature the following transformation equations for the space-time coordinates x'=g(x-vt) t'=t/g g=gamma. Please tell me what do they bring new in the approach to SRT? Thanks

[SOLVED] Linear algebra - transformations Homework Statement Please take a look at: http://www.math.luc.edu/~jdg/w3teaching/math_212/sp02/PDF/test2practice.pdf Please take a look at #7, question c. To determine if the vector w is in the image (range) of T, I find the matrix B that represents...

[SOLVED] Combined linear transformations Homework Statement I have a linear transformation L : R^3 -> R^3 represented by a matrix A. I also have another linear transformation S : R^3 -> R represented by a matrix B. The dimensions of the matrix A must be 3x3 and for B it is 1x3. I have to find...

[SOLVED] Linear algebra - transformations Homework Statement I actually have two questions: 1) I have a linear transformation L and it is represented by a matrix A. I also have a vector w, and I want to find out if w gets "hit" by L - see "answer-part" for my approach, and please comment. 2)...

Homework Statement I have a transformation (not linear! that is what I have to show) F given by: F : P_4 -> P_7 (P_7 is the vector-space spanned by polynomials less than degree 7). I also know that F(p(x)) = (p(x))^2. The matrix A representing F with respect to the two basis is the one I...

Can anyone explain how to derivate "Supersymmetric Transformations" like \phi\rightarrow\psi?? It seems to me that there's no symmetry at all between bosons and fermions. Can anybody know any proofs??

A quick question this time... Example: Let (u,v)=f(x,y)=(x-2y, 2x-y). Find the region in the xy-plane that is mapped to the triangle with vertices (0,0),(-1,2),(2,1) in the uv-plane. Solution: (0,0)=f(0,0), (-1,2) = f(5/3,4/3), and (2,1)=f(0,-1), the region is the triangle with...

A boy stands at the peak of a hill which slopes downward uniformly at angle \phi . At what angle \theta from the horizontal should he throw a rock so that is has the greatest range. Ok, so this is a rotation of the normal x_{1} - x_{2} plane right? So we can use the direction cosines...

Hello, Can someone help me with this problem? Thanks in advance Let T be a linear transformation such that T (v) = kv for v in R^n. Find the standard matrix for T.

1) http://www.geocities.com/asdfasdf23135/advcal13.JPG Let F1 = x^2 - y^2 + z^2 -1 = 0 F2 = xy + xz - 2 = 0 F3 = xyz - x^2 - 6y + 6 = 0 My thought is to compute the gradients, grad F1 and grad F2. Then by taking their cross product, I can get a tangent vector v for the curve. Now, I can feel...

Homework Statement let T: R^{3} -> R^{3} be the mapping that projects each vector x = (x(subscript 1) , x(subscript 2) , x(subscript 3) ) onto the plane x(subscript 2) = 0. Show that T is a linear transformation. Homework Equations if c is a scalar... T(cu) = cT(u) T(u + v) = T(u) +...

Homework Statement Find a basis for the image of the linear transformation T: R^4 -->R^3 given by the formula T(a,b,c,d) = (4a+b -2c - 3d, 2a + b + c - 4d, 6a - 9c + 9d) Homework Equations The Attempt at a Solution Well this question followed asking about the basis for the kernel...

Homework Statement Let A be the matrix of the linear transformation T. Without writing A, find an eigenvalue of A and describe the eigenspace. T is the transformation on R^3 that rotates points about some line through the origin. Homework Equations maybe...Ax=(lambda)x ? The Attempt...

Describe the transformation on the graph of y=1/x needed to obtain the graph of each of the following: a) y= x+3/x+1 b) y= 2x/x-1 im stuck on how to answer this question...how would i solve this?...thanks

Homework Statement Find the inverse Laplace transform of the given functions: 3. \frac{2}{s^2+3s-4} 7. \frac{2s+1}{s^2-2s+2}Homework Equations Inverse Laplace Transform TableThe Attempt at a Solution on 3. i made the denominator look like (s+4)(s-1) but i got lost from there. i couldn't find...

Homework Statement I am trying to show that \vec{e'}_a = \frac{\partial x^b}{\partial x'^a} \vec{e}_b where the e's are bases on a manifold and the primes mean a change of coordinates I can get that \frac{\partial x^a}{ \partial x'^b} dx'^b \vec{e}_a = dx'^a \vec{e'}_a from the invariance...

1. Graph the function f(x)=x^2+4x+3 by starting with the graph of y=x^2 and using transformations. 2. 3. I know the graph opens up, but I don't understand transformations or how to solve them, any help would be greatly appreciated.

Hi. I thought I had tensors and Lorentz transformations under control, but now I'm in doubt again. For example, consider the electromagnetic field tensor F_{\mu\nu} = \begin{pmatrix} 0 & -E_1 & -E_2 & -E_3 \\ E_1 & 0 & B_3 & -B_2 \\ E_2 & -B_3 & 0 & B_1 \\ E_3 & B_2...

Homework Statement A physics professor on Earth gives an exam to her students who are on a spaceship traveling at speed v relative to Earth. The moment the ship passes the professor she signals the start of the exam. If she wishes her students to have time To (spaceship time) to complete the...

what exactly constitutes a gauge transformation? is it a transformation using a differential operator?

Please have a critical look at the lines below: The simplest derivation of the Lorentz transformation simplified: J.M.Levy "A simple derivation of the Lorentz transformation and of the accompanying velocity and acceleration changes," Am.J.Phys 35,615 (2007) arXiv:physics/0603103 revisited.[1]...

divergence question show that the divergence transforms as a vector under 2D rotations. I am so confused abouth what this question wants me to do. Obviously the divergence is not invariant under rotations. Consider the divergence of the function f(x,y) = x^2 * x-hat. The divergence is...