Transformation Definition and 1000 Threads

Hello friend, I want to know how to derive lorentz transformation. Even though i have book that derived lorentz transform,i am not able to understand. I hope you give me an easy derivation of it!

Hello friend, Can you give me an example that shows simultaneous events in one reference frame not simultaneous in other reference frame with the help of lorentz Transformation?

Homework Statement Find the matrix for the transformation which first reflects across the main diagnonal, then projects onto the line 2y+√3x=0, and then reflects about the line √3y=2x Homework Equations Reflection about the line y=x: T(x,y)=(y,x) Orthogonal projection on the x-axis...

Dear all, Poincare transformation construct a group, better to say noncompact Lie group. I want to prove this fact but I don't know how...; I mean the general characteristics- associativity, closure, identity element and inversion element. I would appreciate it if anyone could help me or...

I've been tasked with showing that a Lagrangian under a set of transformations changes by a time derivative. All has gone well, except I'm left with two remaining terms, that I am completely confident, aren't there by mistake (as the 16 terms that should be expected have all popped out with the...

A friend of mine is working with shape memory alloys and he's got one that is behaving strangely. At "low" temperatures a "fresh" solution heat treated sample will form martensite upon cooling, and austenite upon heating as expected. Heat and cool all you want and you get the transformation...

Homework Statement 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...

So, I'm trying (keyword trying) to learn a bit of special relativity on my own via the Stanford lectures on Youtube by Leonard Susskind, but I'm running into a problem. According to the lectures, for two different reference frames with co-ordinates marked (x, t) and (x', t'), the latter...

Homework Statement x2y'' - xy' = ln x Homework Equations The problem I'm having is what do I do with x = et or t = ln x. The Attempt at a Solution I know you have to start with x = et or t = ln x however I'm not sure what to do next...

Can anyone explain to me how I would go about transforming a Cauchy-Euler equation for an equation such as: x2y'' - xy' = ln x I know you have to start with x = et or t = ln x however I'm not sure what to do next...

Homework Statement Evaluate the appropriate determinant to show that the Jacobian of the transformation from Cartesian (this is a typo, they mean spherical) pψθ-space to Cartesian xyz-space is ρ2sin(ψ).Homework Equations The Attempt at a Solution Uhm, I am lost. I'm supposed to prove that when...

Let $T:\mathbb{R}^n\rightarrow\mathbb{R}^n$ be a linear transformation and $R\in \mathbb{R}^n$ be a rectangle. Prove: (1) Let $e_1,...,e_n$ be the standard basis vectors of $\mathbb{R}^n$ (i.e. the columns of the identity matrix). A permutation matrix $A$ is a matrix whose columns are...

Question Consider the linear transformation T(x1,x2,x3)= (2*x1 -2*x2- 4*x3 ,x1+2*x2+x3) (a) Find the image of (3, -2, 2) under T. (b) Does the vector (5, 3) belong to the range of T? (c) Determine the matrix of the transformation. (d) Is the transformation T onto? Justify your answer (e) Is the...

Let V be the linear space of all real polynomials p(x) of degree < n. If p ∈ V, define q = T(p) to mean that q(t) = p(t + 1) for all real t. Prove that T has only the eigenvalue 1. What are the eigenfunctions belonging to this eigenvalue? What I did was T(p)= (lamda) p = q (Lamda) p(t+1) =...

Homework Statement Let V be the linear space of all real functions Differentiable on (0,1). If f is in V define g=T(f) to mean that g(t)=tf'(t) for all t in (0,1). Prove that every real λ is an eigenvalue for T, and determine the eigenfunctions corresponding to λ.Homework Equations The Attempt...

i have a quick question, that is according to the lorentz transformation, the moving frame will have the longer time than the frame in the rest. so is that means if I'm on a moving car for my whole life, my time will greater than those who are in the rest relative to the earth?

Is there a simple way of deriving Lorentz transformation? I don't find the typical derivations in textbook so convincing, which seems to use too many intuitive postulations...

Physics books rarely make the distinction between active or passive Lorentz transformations. The usual Lorentz transformations of the spacetime coordinates in two different inertial frames seem to me to be passive transformations, because by definition passive transformations are coordinates...

Homework Statement Two spaceships A and B are launched from a point X, in opposite directions. At time t=15 minutes, spaceship A crashes. The velocity of the spaceships relative to X is 1.3x10⁸m/s. How far did the collision happen from B, as observed by astronauts on the spaceship...

I would like to get a detailed description, how the world looks for a moving observer in Special Relativity compared to the way it looks for an observer at rest. Do you know any reference, where I can find such a description? Can you maybe even tell me, where to find two pictures of the sights...

Homework Statement |\;| is a norm on \mathbb{R}^n. Define the co-norm of the linear transformation T : \mathbb{R}^n\rightarrow\mathbb{R}^n to be m(T)=inf\left \{ |T(x)| \;\;\;\; s.t.\;|x|=1 \right \} Prove that if T is invertible with inverse S then m(T)=\frac{1}{||S||}. Homework...

$|\;|$ is a norm on $\mathbb{R}^n$. Define the co-norm of the linear transformation $T : \mathbb{R}^n\rightarrow\mathbb{R}^n$ to be $m(T)=inf\left \{ |T(x)| \;\;\;\; s.t.\;|x|=1 \right \}$ Prove that if $T$ is invertible with inverse $S$ then $m(T)=\frac{1}{||S||}$. (I think probably we need...

Homework Statement See attached images below. Homework Equations For attachment "Linear 1," I've proven that it is indeed a linear transformation. My question is what does it mean when it says to show T^2=T? What exactly is the T that I am multiplying by itself? Attachment "Linear...

Homework Statement See attached image below. Homework Equations The Attempt at a Solution I know for it to be a linear transformation it must be that: f(x)+f(y)=f(x+y) and f(tx)=tf(x) where t is a scalar. I'm not sure where to start with this proof.

Homework Statement Let V = F^n for some n ≥ 1. Show that there do not exist linear maps S, T : V → V such that ST − T S = I. The Attempt at a Solution I used induction to prove that ST^n-T^nS = nT^n-1 and that S^nT-TS^n=nS^n-1, and I know I'm supposed to use that to come up with a...

Hey mobius transformation defined as f(z) = \frac{az+b}{cz+d} and ad \ne bc it is a one to one function how i can find a mobius transformation that take the real line into the unit circle I read it in the net f(z) = \frac{z - i}{z+i} and i checked it, it takes the real line into the...

Homework Statement I am trying to prove that Maxwell's laws are consistent with special relativity if one frame is moving in the x direction with another. Homework Equations In this case, I know that \frac{\partial}{\partial x'} = \gamma \frac{\partial}{\partial x} + \frac{\gamma v}{c^2}...

Homework Statement Consider the three operators defined by $$\left(S_i\right)_{jk} = -i\epsilon_{ijk}$$ in the x-y-z space and the basis vectors given in x-y-z space as $$e^{\left(1\right)} = -\frac{1}{\sqrt{2}}\left(e_x + ie_y\right), e^{\left(0\right)} = e_z, e^{\left(-1\right)} =...

There's this theorem: A linear map T: V→W is one-to-one iff Ker(T) = 0 I'm wondering if there's an analog for showing that T is onto? If so could you provide a proof? I'm thinking it has something to do with the rank(T)...

Homework Statement Let T: R3 -> M22 by T\begin{bmatrix} a \\ b \\ c \label{T} \end{bmatrix} = \begin{bmatrix} a-b & b-c \\ a+b & b+c\\ \end{bmatrix} Is this transformation one-to-one? Homework Equations The Attempt at a Solution I am not really certain...

Hi all! Another questions which is due to the gaps in my calculus knowledge. In these notes: http://people.hofstra.edu/Gregory_C_Levine/qft.pdf in the line above eq. (1) where it says that notation P is now unecessary, is it because \partial{ (p+\delta p)} is much smaller than p+\delta p...

Homework Statement Please see attached files and let me know if I am correct or not. Homework Equations The Attempt at a Solution

Hello all, I am searching for an analytic solution to an integral of the following form: I[q',k\rho\,]=\frac{1}{\pi}\int_{0}^{2\pi}e^{jq'(\phi-\phi_0)}e^{-jk\rho\sin(\phi-\phi_0)}d\phi In this equation, q' is real and k\rho is real and positive. Also, the following integral is closely...

Homework Statement Describe the possible echelon forms of the standard matrix for the linear transformation T. T: |R3 --> |R4 is one to one. The Attempt at a Solution T(x)=Ax. Right? So A must be the standard matrix. I got this: A = | £ * * | | 0 £ * | | 0 0 £ | | ? ? ? | Where £...

1. The question Let V be a vector space with the ordered basis β={v1, v2,...,vn}. Define v0=0. Then there exists a linear transformation T:V→V such that T(vj) = vj+vj-1 for j=1,2,...,n. Compute [T]β. Homework Equations [T]γβ = (aij), 1≤i≤m, 1≤j≤n (where m is dimension of γ and n is the...

Hi everyone, I am trying to solve the following problem. Is there exist a transformation matrix T, different then the block diagonal, with all blocks the same, such that the form of the matrix A=[A1 A2 ; I 0], is preserved? All blocks of A are in R^{nxn}, I is identity and 0 is zero matrix. In...

Homework Statement http://imageshack.us/a/img26/8403/homeworkprobsg28.jpg a. Use source transformations to find the voltage V0 in the circuit (green). b. Find the power developed by the 250V voltage source c. Find the power developed by the 8A current sourceHomework Equations V = IR KVL...

I'm using a book that has a loot of errors (luckly most of them are easy to recognize, like a = instead of a ≠ or viceversa, but some are way more serious), and I'm not sure if it's a new error or a thing I don't understand. Either I didn't understood all the steps of the proof or the correct...

Here is the question: Here is a link to the question: Projection and linear transformation? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Homework Statement So I have this laplace transformation chart and was a bit unsure about the laplace and inverse laplace of this. The unit step function, where u(t) = 0 where t < 0, u(t) = 1 where t > 0. The laplace transformation chart that I have has two columns, the column on the...

Homework Statement Let T:P_m(\mathbb{F}) \mapsto P_{m+2}(\mathbb{F}) such that Tp(z)=z^2 p(z) . Would a suitable basis for range T be (z^2, \dots, z^{m+2}) ?

Transformation of stresses in beer and johnston mechanics of materials. While reading the section on trsnformation of stresses they have solved by using the force components in x' and y' directions. I have attached a screenshot of the relevant page and the figure. I have few doubt as to how the...

Homework Statement Let T be a linear transformation from R3 to R3. Suppose T transforms (1,1,0) ,(1,0,1) and (0,1,1) to (1,1,1) (0,1,3) and (3,4,0) respectively. Find the standard matrix of T and determine whether T is one to one and if T is onto Homework Equations The Attempt...

Greetings, My question is from the book "Tensor Analysis" by Barry Spain. I am asked to show that how a vector transforms from rectangular Cartesian coordinates to polar coordinates. I have attached the question in jpeg format. I have came up with a solution but the angular component in my...

Hi guys, I am having a very stupid problem. I can't figure out what Mobius transformation represents T(z)=z*, where z* is the complex conjugate of z. In my book we are learning about Mobius transformations and how they represent the group of automorphisms of the extended complex plane (Ʃ). [...

Hi all, I have been reading up about continuum mechanics recently, and have a question regarding the reduction in stiffness coefficients in the stiffness matrix. I am aware of how the stiffness matrix is reduced to 21 coefficients. However, in order to reduce it from 21 to 13, one has to...

Homework Statement The problem asked us to show that the Euler-Lagrange's equations are invariant under a point transformation q_{i}=q_{i}(s_{1},...,s_{n},t), i=1...n. Give a physical interpretation. Homework Equations \frac{d}{dt}(\frac{\partial L}{\partial \dot{s_{j}}})=\frac{\partial...

Homework Statement Show that the Lagrangian \mathcal{L}=\frac{m}{2}\vec{\dot{r}}^2 \, \frac{1}{(1+g \vec{r}^2)^2} is invariant under the Transformation \vec{r} \rightarrow \tilde{r}=\vec{r}+\vec{a}(1-g\vec{r}^2)+2g\vec{r}(\vec{r} \cdot \vec{a}) where b is a constant and \vec{a} are...

Hi All, I have a problem in understanding the concept of dirac delta function. Let say I have a function, q(r,z,t) and its defined as q(r,z,t)= δ(t)Q(r,z), where δ(t) is dirac delta function and Q(r,z) is just the spatial distribution. My question are: 1. How can I find the time derivative...

Hi, Homework Statement How may I find (or prove that there isn't) a linear transformation which satisfies T: R3->R1[x], ker T = Sp{(1,0,1), (2,-1,1)}? Homework Equations The Attempt at a Solution I am not sure how to approach this. I understand that kerT is the group of all...