Transformations Definition and 823 Threads

I quote a question from Yahoo! Answers I have given a link to the topic there so the OP can see my response.

Hi, From perusing books on QFT, I've gathered that the photon is written as a 4-vector in field theory and transforms under the standard Lorentz group operators, while an electron for instance is a 2-component spinor and transforms under a special representation of the Lorentz group as part of...

Hi, Let f be a linear transformation over some finite field, and denote f^{n} := f \circ f \circ \cdots \circ f, n times. What do we know about the linear maps f such that there exist an integer n for which f^{N} = f^n for all N \geq n? Also, how about linear maps g satisfying g = g \circ f^i...

Background For which of the invertible transformations (\mathbf{q}, \mathbf{p}) \leftrightarrow(\mathbf{Q}, \mathbf{P}) \mathbf{Q}(\mathbf {q}, \mathbf {p}, t) \mathbf{P}(\mathbf{q}, \mathbf {p}, t) is it so that for every Hamiltonian \mathcal{H}(\mathbf {q}, \mathbf {p}, t) there is a...

For a linear transformation to be invertible, is it a requirement that the domain and codomain be the same vector space, or merely that they have the same dimension? My intuition tells me they merely need the same dimension but someone can correct me please? BiP

Homework Statement Find an orthogonal transformation ##\mathbb{R}^{3}\rightarrow \mathbb{R}^{3}## that map plane ##x+y+z=0## into ##x-y-2z=0## and vector ##v_{1}=(1,-1,0)## into ##(1,1,0)##. Count all of them! Homework Equations ##A_{S}=PA_{0}B^{-1}##The Attempt at a Solution So basis...

Consider the operation of multiplying a vector in ℝ^{n} by an m \times n matrix A. This can be viewed as a linear transformation from ℝ^{n} to ℝ^{m}. Since matrices under matrix addition and multiplication by a scalar form a vector space, we can define a "vector space of linear transformations"...

Ahoy, I was reading parts of Weinberg's QFT book vol. I and was surprised at his definition of a scalar field or Lorentz transformations on fields in general. Usually (e.g. Maggiore, Modern Intro to QFT) I see the scalar field defined as Lorentz transforming via \Phi'(x') = \Phi(x) \text{...

I'm just having trouble understanding some of the notations given, when attempting questions such as the following: {f\inF(ℝ,ℝ): f(3)=5}. Is it just saying that, the function 'f' spans all real values?

Homework Statement Two light flashes occur on the laboratory x axis, the first at time t=0 and position x=450 m, the second at time t=+1 ms, at the origin. In an inertial frame moving along the x-axis with speed v, the events are simultaneous. What is the speed v? Homework Equations...

I am not sure if I have the title right, but here is my problem: I have a ray which 'should be' shot vertically from a point p, but depending on the situation it can: 1) either be shot in any direction in the hemisphere above p 2) shot with an angle of no more than σ off the vertical 3) shot...

$$y_{1}=2x_{2}$$ $$y_{2}=x_{2}+2$$ $$y_{3}=2x_{2}$$ I know that in order for a transformation to be linear it has to satisfy: I) $$T(v + w) = T(v) + T(w)$$ II) $$T(kv) = kT(v)$$ But what are v and w in this case? note: v and w are vectors and are suppose to have arrows on top of them but I...

Homework Statement Let T: R3--> R4 be a linear transformation. Assume that T(1,-2,3) = (1,2,3,4), T(2,1,-1)=(1,0,-1,0) Which of the following is T(-8,1-3)? A. (-5,-4,-3,-8) B. (-5,-4,-3,8) C. (-5,-4,3,-8). D.(-5,4,3,-8) E (-5,4,-3,8) F. None of the above.Homework Equations I really have no...

I'm trying to follow Feynman's explanation on page 26-10 of Volume 2 of The Feynman Lectures on Physics. He describes the electric and magnetic fields in a FoR S' moving between the plates of a condenser. Feynman writes that we see a reduced E and an added transverse B in S'. I've attached a...

Hey So, I was wondering how to convert from one coordinate axes to another... in particular, where the new axes are y = x and y = -x, as seen by the picture below I want it so that the Red dot in the new coordinate system will be (\sqrt2,0). Is there an easy way to do this? (My lookings on...

Q Applying a horizontal stretch by a factor of k (where k is a constant such that k>1) to f(x)=lnx is equivalent to applying what shift to f? Give both the amount and direction of the shift. my A so i came to the conclusion that the answers must have to do with the laws of logs. and from...

Suppose we have the double integral of a function f(x,y) with domain of integration being some rectangular region in the 1st quadrant: 0≤a≤x≤b, 0≤c≤y≤d. Would the following transformation generally be acceptable? (I've quickly tried it out several times with arbitrary integrands and domains...

FIRST OFF: Sorry for the multiple post on this subject, I couldn't figure out how to edit my first post on this topic (I promise I'm not spamming!) Homework Statement Homework Equations The Attempt at a Solution Step 1: Removed unnecessary resistors R1 and R3. R1 is removed...

Why is a linear transformation T(x)=Ax one-to-one if and only if the columns of A are linearly independent? I don't get it...

Homework Statement Describe the transformations that must be applied to the graph of y = 5^x to obtain the graph of y = 2 - 3(5^(x+4)) and complete the following table (attached) Homework Equations y = ab^k(x-4) + c The Attempt at a Solution I started filling out the table. First...

Homework Statement First part of the problem: Newton’s second law is given by F=dp/dt. If the force is always perpendicular to the velocity, show that F=gamma*m*a, where a is the acceleration. Second part of the problem: Use the result of the previous problem to show that the radius of a...

URGENT: Delta-Wye transformations Hello there. In my electrical fundamentals class (a 201 level class), we just barely started Delta-Wye transformations. However, the homework that is due online tonight uses full transformations...confused, I have just tried to work through this using the book...

Homework Statement Two particles in a high-energy accelerator experiment are approaching each other head-on, each with a speed of 0.9500c as measured in the laboratory. What is the magnitude of the velocity of one particle relative to the other? Homework Equations...

Hi, Homework Statement I wish to pose a few questions I have concerning transformations: (1) I am trying to disprove the following statement: Let T: V->U be a linear transformation between vector spaces V and U, and let {v1,...,vn} be a set of vectors in V. If {Tv1,...,Tvn} spans U, then...

Hello guys, I'm studying Thermodynamics and I don't totally see how you introduce the potencials using Legendre transformations. I have seen a non formal explanation showing how you can interpret them, but not a rigorous demonstration of how you get them via the Legendre transformations...

This may be vague, so I apologize. I am interested in applied mathematics, so my question is about the process a scientist or engineer uses to determine what differential equation to use for a non-linear process. I am not familiar enough with describing non-linear processes to be able to...

Suppose I have the following transformation: u = \frac{x}{x^2+y^2+z^2} v = \frac{y}{x^2+y^2+z^2} w = \frac{z}{x^2+y^2+z^2} Is there a fast way to calculate the determinant jacobian without having to deal with the whole 3x3 determinant? I noticed that the inverse...

Let T : R2 -> R2 and S : R2 -> R2 be linear transformations defined by: T(x; y) = (5x + y ; 2x + 2y) and S(x; y) = (3x + 2y ; x): (i). Find the image of the line 2x + 3y = 5 under T. (ii). Find the natural matrices of the linear transformations T o S and T^-1 Sorry, I haven't done...

Homework Statement Let T_1,T_2:ℝ^n\rightarrowℝ^n be linear transformations. Show that \exists S:ℝ^n\rightarrowℝ^n s.t. T_1=S\circ T_2 \Longleftrightarrow kerT_2\subset kerT_1 . The Attempt at a Solution (\Longrightarrow) Let S:ℝ^n\rightarrowℝ^n be a linear transformation s.t...

this isn't really homework, but I was just wondering if someone could offer an intuitive reason as to why when random variables are transformed, we use absolute values of derivative of those functions, as opposed to the functions themselves?

Hi all, I have a question that seems very simple but I just do not see it;) Let α denote an r×1 vector with arbitrary entries; I'm trying to construct an 1×r vector m such that αm = I, where I is the r×r identity matrix... The first question is: is this possible? I tried the...

Homework Statement Two identical samples of ideal gas are initially at P1 and V1. The first sample undergoes an isothermal transformation to P2, V2 and second sample undergoes an adiabatic transformation to P3, V2. If P3<P2, is V2 higher or lower than V1? Explain Homework Equations...

In a book ("The special theory of relativity by David Bohm") that I'm reading, it says that if (x,y,z,t) are coordinates in frame A, and (x',y',z',t') are coordinates in frame B moving with v in realtion to A, if we have (for a spherical wavefront) c^2t^2 - x^2 - y^2 - z^2 = 0 and we...

My prof uses this all over his notes, and I'm still not 100% sure what he means by it: C[T]B or B[T]B From what I can gather, it has something to do with a transformation matrix, but where the B and C come into play, I have no idea.

Hey guys, I'm studying these concepts in linear algebra right now and I was wanting to confirm that my interpretation of it was correct. One to one in algebra means that for every y value, there is only 1 x value for that y value- as in- a function must pass the horizontal line test (Even...

I'm currently working through Griffith's book Introduction to Elementary Particles, and studying the chapters on gauge theories. From classical E&M, I understand what we mean by a gauge transformation and why the Lagrangian must be invariant under such a transformation, but what I don't...

Hi all, So this question is fairly basic, but I want to be certain I have the right idea before I do the other parts (asks about it in standard basis etc). It's a book question: Homework Statement Here are the vectors : u=[ 1 2 0] v=[2 5 0] w=[1 1 1] This forms a basis B of R3...

In a desparate attempt, not for the first time, to understand some issues on coordinate transformations in GR from a passive and active point of view, I opened this thread. I already read references of Wald, Rovelli and others, (actually, I think I saw almost all articles and notes which try to...

In the last question in this link: http://pages.uoregon.edu/csinclai/teaching/Fall2009/files/hw8.pdf 1) I did not understand how they got the region for y1, y2, and y3... 2) How would the solution be different (or not possible) if X1, X2, and X3 were not iid? Thanks in advance

1. If multiplication by A rotates a vector X in the xy-plane through an angle (theta). what is the effect of multiplying x by A^T ? Explain Reason.

This thread is posted to examine the proposition that all matrices define linear transformations. But what of the matrix equation? \left[ {\begin{array}{*{20}{c}} 0 & 1 & 0 \\ \end{array}} \right]\left[ {\begin{array}{*{20}{c}} {blue} \\ {red} \\ {green} \\...

If we have a linear transformation T:W -> W. Then if we write T with respect to a different basis B, will the domain and range still be W? So, will we have [T]_B : W \rightarrow W ? If not, can anybody explain to me why? Thanks in advance.

My book has introduced the idea of gauge invariance in terms of classical electrodynamics (attached file). However, I am not sure I completely understand how it works. On the one hand they use a lot of time on specifying how you can add to the vector potential the gradient of any scalar, whilst...

Homework Statement The problem is attached. The problem statement is to "determine whether the function is a linear transformation between vector spaces." Homework Equations N/A The Attempt at a Solution T(0)=[1 0 0]^t ≠ 0, thus T is not linear. Did i do that right? It seems...

Starting with: x'=\gamma(x-vt) & x=\gamma(x'+vt') I know that I can derive t'=\gamma(t-vx/c^2)... however I can't seem to make it fall out mathematically. The suggested method is to cancel x'. Can anyone help me out on the steps? Much appreciated! :)

Hello PF! Homework Statement The graph of the function y = 2x2 + x +1 is stretched vertically about the x-axis by a factor of 2, stretched horizontally about the y-axis by a factor of 1/3 and translated 2 units right and 4 units down. Write the equation of the transformed function Homework...

I'm taking a quantum field theory course and the topic of active vs passive transformations came up. I have previously taken a physics course and active/passive transformations were never explicitly discussed. What is the difference between the two? In particular I'm trying to follow the...

Homework Statement Im not sure what each of the variables do in y=cax-p +q Homework Equations The Attempt at a Solution my understanding is that -q is for vertical shifts/transformations -p is for horizontal shifts/transformations -and c is for vertical stretching not...

Homework Statement An electron and a positron are observed from the lab to move in opposite directions with a speed of 0.5c and 0.7c, respectively. Find the speed of the positron when observed in the electron's rest frame. Homework Equations in attached PDF The Attempt at a...

Hi. I am trying to understand a statement from Peskin and Schroeder at page 59 they write; "The one particle states |\vec p ,s \rangle \equiv \sqrt{2E_{\vec p}}a_{\vec p}^{s \dagger} |0\rangle are defined so that their inner product \langle \vec p, r| \vec q,s\rangle = 2 \vec E_\vec{p}...