Transformations Definition and 863 Threads

"Let T be a linear transformation on a finite dimensional real vector space V. Show that T is diagonalisable if and only if there exists an inner product on V relative to which T is self-adjoint." The backward direction is easy. As for the forward direction, I don't understand how given an...

I was wondering if one of the approaches to proving the RH involves limits of mobius transformations of the zeta function on the right side of the imaginary axis such that all the non-trivial zeros get mapped into an annulus; this annulus is then shown to contain an infinate number of zeros via...

Hi the following assigment. Given P_{2} (D) be a vector space polynomials of at most degree n=2. Looking at the transformation T: P_2(D) \rightarrow D^2, where T(p) = [p(-i),p(i)]. 1) Show that this transformation is linear. I order to show this I hold my transformation up...

This is the problem: Let T be a complex linear space with a complex inner product <.,.>. Define T in L(V,V) to be Hermitian if <Tv,v> = <v,Tv> for all v in V. Show that T is Hermitian iff <Tv,w> = <v,Tw> for all v,w in V [Hint: apply the definition to v+w and to v+iw]. So this was my...

Problem 1.10(a) of DJGriffiths asks: "How do the components of a vector transform under a translation of coordinates?" This is confusing me (not hard to do) since the translation is given, then isn't it just: x' = x + A where A = \left(\begin{array}{c} 0 \\ -a \\ 0 \end{array}\right)...

My question is: If P' is the image of P under a matrix D = (1, -4, 0, -1) as follows (top left, top right, bottom left, bottom right). If P is not on the x-axis, why is PP' bisected by the x-axis and is at a constant angle to the x-axis, for any choice of P? :confused: I can visually see...

I just wanted to know how I could work out the angle of rotation from the following matrix -0.6, -0.8 (top) and 0.8, -0.6 (bottom)? :frown: Is this possible or am I missing something here?

http://img499.imageshack.us/img499/9875/untitled1copy0oi.jpg Hello everyone I'm not looking for someoene to tell me the answer, but I'm really confused on how you can tell if somthing is a linear stransformation or not? I'm not understand what operations I'm suppose to go through to find...

I have an assignment problem and I don't even know where to start... I'm taking the course through correspondence so i have no notes or prof to talk to... I've read my text and course manual over and over again but I just can't figure it out Let T: P2->P2 be a linear transformation defined by...

A question reads: Let T: V-->W be a linear transformation. a) If T is one-to-one and TR=TR1 for transformations R and R1: U -->V, show that R = R1 b) If T is onto and ST=S1T for transformations S and S1: W -->U, show that S=S1 I am sooo very lost here, and no idea where to start:(...

i think I'm just having a hard understanding linear transformations... i was asked if (5, 0) is a vector in R(T) given by the formula T(x,y)=(2x-y,-8x + 4y)...i really don't get what I'm supposed to do here.. any hints would be most appreciated.

I'm just wondering if someone can let me know if I'm on the right path here... this question asks to show that the Function T: R^3 ----> R^2 given by the formula T(X1, X2, X3) = (2X1 - X2 + X3, X2 - 4X3) is a linear transformation. soln' the definition of a L.T. is that T(u + v) = T(u)...

Hi, can someone help me get started on the following question? Q. Show that there is no line in the real plane R^2 through the origin which is invariant under the transformation whose matrix is: A\left( \theta \right) = \left[ {\begin{array}{*{20}c} {\cos \theta } & { - \sin \theta...

Okay, I will just admit that I stink at using mathematical proof in Linear. I hope someone can give me a push with this problem Prove that T : R(real)^3 -> R(real)^3 defined by T([yz,xz,zy]) is not a linear transformation. Reading my book I know that I need to prove that the...

hello everyone can anyone give me any tips on recognizing compressions and expansions of functions? ie. vertical expansion, horizontal compression

Can anyone at least tell me how to get started on this problem I have? Problem: Determine whether the following are linear transforatmions from P2 to P3. L(p(x)) = xp(x) I understand when it's in vector form but not really picking up on the polynomial part of this.

hi everyone I have trouble recognizing expansions/compressions, and not knowing how draw graphs of recipricol transformations (of functions). can someone explain to me how to "do" them? or recommend a site that has a tutorial about it? thanks in advance.

hi everyone I have trouble recognizing expansions/compressions, and not knowing how draw graphs of recipricol transformations (of functions). can someone explain to me how to "do" them? or recommend a site that has a tutorial about it? thanks in advance.

The Dirac equation can be derived from the transformation properties of spin-1/2 systems under pure boosts. This derivation is presented Ryder's Quantum Field Theory. However, the derivation of a similar equation for spin-1 systems is not given. Following the same steps as in Ryder for the Dirac...

So often students question the validity of the twin paradox and how acceleration is involved in looking at round trip scenarios that I am asking why not just give them the tools to transform between the coordinates of an inertial frame and those of an accelerating frame. It is not hard to do and...

These problems are actually for my classical mechanics class, but they are linear-algebra based. I can construct a transformation matrix, but I have trouble visualizing the rotations, particularly in 3-space. So if someone could help me get a pictorial idea of what's actually happening, then...

Alright, this is my case. I am now a former International Baccalaureate Diploma programme student that wrote my extended essay in mathematics. As far as it seems, I was incredibly unlucky when they corrected my essay, cause as it seem, the word count was too much, so they kind of didn't read my...

Unique linear transformations! Problems agiain :cry: :cry: :cry: Say I have 2 vector spaces with some finite number of vectors(can assume linear independency)...how can I show that the linear transformation between the two is unique? Thanks in advance!

can ne 1 explain 2 me the basics of lorentz transformations...mathematically i know how things transform bt i want a more revealing explanation ...relate it 2 boosts and rotations also ... thanx

Hello. I am given the following: T([1,2,-3]) = [1,0,4,2] T([3,5,2]) = [-8,3,0,1] T([-2,-3,-4]) = [0,2,-1,0] And of course I know that: T(x) = Ax and I want to find the matrix A. So, from the individual equations, I construct: A[1, 2, -3] = [1, 0, 4, 2] (please forgive, these...

Time invariance implies conservation of energy. Space invariance implies momentum convervation. What convervation law does the Lorentz invariance imply?

What is the signifigance of the first derivative of the Lorentz transformation gamma function with respect to dv? What type of system does this derivative represent? \gamma'(v) = \frac{d}{dv} \left( \frac{1}{\sqrt{1 - \left( \frac{v}{c} \right)^2}} \right) = \frac{v}{c^2 \left[ 1 - \left(...

Hello, I'm looking for a good Dynamics Book. I got Engineering Mechanics: Dynamics by Andrew Pytel and Jaan Kiusalaas, but it's fairly introductional, i also got Classical Mechanics by Goldstein, which is advanced. I am looking for intermediate level. I am looking mainly to learn the Lagrange...

Could someone please explain me what are Möbius transformations, and what do they work for? Where can I find more info about this? Thanks in advance.

I've uploaded a document which I am currently working on. I would like to verify if I am doing these problems correctly. Thank you. In the first attachment (3.4b) For 1. a. 4x^3-2x b. T(P)=0 ker T={C:C \inR} Im T = {P|P is less than degree 3 or less} c. T is not one to one because P...

Gents, Could you please help me: Speaking about General Coordinate Transformations, one speaks always generally. Are there any explicit expressions for General Coordinate Transformations? Like in SR speaking about Lorentz Transfrmations one recalls Lorentz Matrixes. Maybe I'm not quite...

I have recently just been given a computer lab task and that is to research transformations on the net and write a 1 page essay about them, which i am finding hard to find information on them, but anyway, here is my problem. We are required using our classes data to do transformations of our...

I'm having trouble understanding the concept of laplace transformations. my book states that it is comparing how much a function y(t) is like a standard function. what exactly does the answer mean such as y(s)=1/(s-2) is this the differnence between the functions depending on the value of s...

Linear Transformations Rn-->Rm Question I would be very grateful if someone can explain what is going on in the following problem: Determine whether the following T:Rn to Rm T(x,y)=(2x,y) Solution from solutions manual: T((x1,y1) + (x2,y2)) = (2(x1+x2), y1+y2) = (2x1,y1) + (2x2,y2)...

Evaluate \int\int_{R} \left(2x^2 - xy - y^2\right) dx\;dy by applying the transformation u = x - y , v = 2x + y for the region R in the first quadrant bounded by the lines y = -2x + 4, y = -2x + 7, y = x - 2, y = x + 1 I don't even know where to start! Please help.

This is a question I found no answer from books. Is Connectedness and Simply-connectedness preserved by Canonical Transformations? If an area in phase space is connected (simply connected), will it still connected (simply connected) in the new phase space of new canonical variables?

We know that a transformation from V to W is linear if the following hold: 1.) For every x, y in V, T(x+y) = T(x) + T(y) 2.) For every x in V and for every a in R (real numbers), T(ax) = aT(x) I need two nonlinear transformations from R to R. One must satisfy #1 above and violate #2. The...

Okay, is it possible to transform an "x-y" equation into a parametric "equation"? If so, how would I go about it? For example, if I am given the equation (x^2)/1-(y^2)/25=1, what process would I have to use to find the Parametric equations? Thank You.

Hi. I’ve just started learning about tensors on my own and am still trying to understand coordinate transformations. If I begin with a vector whose Cartesian components are (x, y, z) and apply the tensor transformation to cylindrical polars, I end up with (r, 0, z) – is this right? I...

sorry, I'm not particularly well versed in this field. can someone explain the lorentz transformations to me?

Prove that if T:R^{m} \rightarrow R^{n} and U:R^{n} \rightarrow R^{p} are linear transformations that are both onto, then UT:R^{n} \rightarrow R^{p} is also onto. Can anyone point me in the right direction? Is there a theorem that I can pull out of the def'n of onto that I can begin this proof?

Could anyone provide a derivation of the Lorentz transformations for me? And if the Lorentz transformations existed before Einstein came up with special relativity, then why wasn't the Lorentz guy able to come up with special relativity? It seems to me that he did all the work in showing that...

I am going to try to explain relativity without light or maxwell's equation. Light or Maxwell's equation or electromagnetism has nothing to do with relativity. a) The speed of light (and not light itself - note the difference) has something to do with it. b) The fact that M&M used light...

applications ? We are studying linear transformations right now in my Lin. Alg. class. And I like to think that mathematics has some application in the real world. But what kind of appliation do matrix transfomations have? Are there any algorithms based on it? If not, it's kind of pointless in...

We are doing linear transformations in geometry. We have a projection in three dimensional space onto a line. Do we basically treat this as the same as a two dimensional projection? Also, anyone know of a really good linear algebra textbook that you could basically teach yourself from? I'm...

Im a second semester engineering student and I am a few weeks into a linear algebra class. I understand most of it, but my teacher has to work to speak english so she doesn't explain things very well. We just started linear transformations and a few things seem unclear to me. Take a shear...

In all the textbooks I read on SR, they always list the LT assuming y'=y and z'=z. But how does the time coordinate transform if the speed has a y and a z component? I'm guessing t' = \frac{t-(v_x x + v_y y +v_z z )/c^2}{\sqrt{1-v^2/c^2}}

Hello out there, I have a question about the transformation of discrete random variables. I have a joint pdf given by: f(x,y)=\frac{(x-y)^2}{7} where x = 1, 2 and y = 1, 2, 3 I can easily create a table summarizing the joint pdf of RVs X and Y, f(x,y). I now have a transformation...

Let S:V --> W and T:U --> V be linear transformations. Prove that a) if S(T) is one-to-one, then T is one-to-one b) if S(T) is onto, then S is onto This makes intuitive sense to me, since S(T) maps U to W, but I can't figure out how to go about proving this. I would appreciate any help...

Linear transformations and rotations... Hi everyone. I need some help getting started on this question. Let R: R3 ---> R3 be a rotation of pi/4 around the axix in R3. Find the matrix [R]E that defines the linear transformation R in the standard basis E={e1, e2, e3} of R3. Find R(1,2,1)...