Transformations Definition and 823 Threads

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)...

Hi , I'd like to know if anybody could help me understand the following: I was following the following derivation of the Lorentz transformations (http://vishnu.mth.uct.ac.za/omei/gr/chap1/node4.html) and i managed to understand everything except possibly the most crucial step...how does one get...

Ok I need some help. I have. t=\frac{t_0}{\sqrt{1-\frac{v^2}{c^2}}} and i rearrange to get: v=\sqrt{c^2(1-\frac{t_0^2}{t^2})} Ok I am setting C=1 tnot = 518400 t = 4.7304 *10^17 as you can imagine my answer i know will be .999999999999 with a lot of 9'sV. The problem is...

We have just recently been doing transformations of sin and cos graphs, but we must find out transformations of logarithm graphs. A typical log function could be log (x). What i want to know is, when you change the base, what would happen to the graph, when you put a number out the front...

Hey people, I just finished reading a chapter in a book on quantum mechanics that has deeply disturbed me. The chapter was about symmetry in quantum mechanics. It was divided in two basic parts: time dependent and time independent transformations. Time independent transformations were...

I'm kind of stuck with the xf(0), hope this is the right place for this question? let L(f) = 2Df - xf(0) is L a linear transformation on the space of differentiable functions? thanks for your help Philip

I'd like to check my proof. It seems easy enough, but I'd like to make sure that I'm not missing anything: If V is the space of all continuous functions on [0,1] and if Tf = integral of f(x) from 0 to 1 for f in V, show that T is a linear transformation From V into R1. Like I said the...

Something has me puzzled about the theory of relativity. At time 0, a photon is emitted from the origin of a rectangular coordinate system. At time t, the photon is at position x, on the positive x axis. Therefore in amount of time t-0=t, the photon has traveled a distance of x. The speed...

Hey guys What exactly are the Lorentz transformations? In the "Was Einstein a genius" thread, it looks like the transformations were known before Einstein had SR/GR?

Im sorry. I am really new to this. Whats the Difference between FT and LT ?

im working on these, and I am supposed to find the image of a set under a given transformation. can someone please explain to me a good way of doing this?

Let g(x) belonging to Pn-1(R) be an arbiitrary polynomial of degree n-1 or less. Show that there exists a polynomial f(x) belonging to Pn(R) such that xf''(x)-f'(x)=g(x)" I interpreted this question as having to prove the linear transformation T: Pn(R) --> Pn-1(R) where f(x) |-->...

In the "intro to differential forms" thread by lethe, Super Mentor Tom defines a vector as something that transforms under rotation (multiplication by an orthogonal matrix) and parity (reflection through a mirror) in a certain way. I'm currently reading "Introduction to Vector and Tensor...

In a vector space R^3, is given a transformation A with a subscript A(x1,x2,x3)=(2*x1+x2, x1+x2+2*x3, -x2+x3). Linear transformation B has in the basis; (1,1,1), (1,0,1), (1,-1,0) a matrix T: [-1 2 3] [ 1 1 0]...