I did the problem but I just need to make sure I did it correctly.. If I did it incorrectly, please let me know.
Homework Statement
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Homework Equations
Problem 4 a-d
The Attempt at a...
Hi, I'm working through Schutz's intro to GR on my own, and I'm trying to do problems as I go to make sure it sinks in. I've encountered a bump in chapter 5, though. I don't think this is a tough problem at all, I think it's just throwing me off because x and y are coordinates as well as...
Homework Statement
Let T: R3 - R3 be the linear operator given by
T = -y + z
-x + z
x + y
Find a basis B' for R3 relative to which the matrix for T is diagonal using the standard basis B for R3.
Homework Equations
[T]B' = P-1[T]BP
The Attempt at a Solution...
I am currently doing a course on Computer Graphics Algorithms. This involves lot of matrix transformations i.e. for eg - rotating co-ordinates, translating, reflecting etc.
I am solving the problems on paper using a calculator, but I need some software which will help me verify the solution...
Homework Statement
Let T: P2 - P2 be the linear operator defined by
T(a0 + a1x + a2x2) = a0 + a1(x - 1) + a2(x - 1)2
(a) Find the matrix for T with respect to the standard basis B = {1, x, x2}.
Homework Equations
[T]B[x]B = [T(x)]B
The Attempt at a Solution
T(1) = a0 + a1(1 -...
oblique and horiz asymptotes, axis same transformations and other things.
i do not understand these at all and the text makes no sense (see attachment).
i can find the asymptotes of all types, but i do not understand how the methods i use work. please explain the methods and the reasoning...
Thanks for reading!
Homework Statement
I have been given a proof for the lorentz transformations (which I only partly understand) that relied on the two relativity postulates (equivalence of inertial systems and the speed of light being constant) for the case of two standard inertial...
In school I've always learned that tensor transformations took the form of:
\mathbf{Q'}=\mathbf{M} \times \mathbf{Q} \times \mathbf{M}^T
However, in all the recent papers I've been reading. They've been doing the transformation as:
\mathbf{Q'}= \frac {\mathbf{M} \times \mathbf{Q}...
I'm slowly trying to understand sp relativity. I admit I got lost in the last thread I posted :blushing:. But thanks to all who replied!
I have a question about the Lorentz transformations formulas. This is more of a mathematical question about how the formulas are derived.
If you have...
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 leaves H invariant. Show...
While it's pretty easy to derive the infinitesimal version of the special conformal transformation of the coordinates:
x'^{\mu}=x^{\mu}+c_{\nu}(x^{\mu} x^{\nu}-g^{\mu \nu} x^2)
with c infinitesimal,
how does one integrate it to obtain the finite version transformation...
I've studied classical physics and never heard this before until recently...the allowable coordinate transformations for classical mechanics are rotations and translations. Could someone explain why this is so? What makes these "allowable" (I know they are orthogonal transformations).
Hi,
I am confused about a lot of Fourier transformations:
A Fourier transform with variable f
A Fourier transform with variable e^{jw}
Fourier series
What is the difference between these different Fouriers?
Another thing, when does the convolution in the time domain become a multiplication...
In SRT, Force (F) transforms identically to d(mV)/dt, which can in turn be transformed using the Lorentz transformations and the dependence of m upon speed. This raises the question whether Force in the force laws also transforms the same way among different reference frames. Certainly the...
Many equations are affected by Lorentz transformations. Time, mass, volume of a moving object, momentum, force etc. I want to know if the following equations are affected by Lorentz transformations:
1. Distance=velocity*time (r=vt)
2. E=hv
3. j*=ot
4. F=G*m1*m2/r^2
Also, is the Newton's...
Hi, I've been breaking my head on the matrix form of the lorentz transformation between one set of coordinates in one inertial frame (t,x^1,x^2,x^3) and what those coordinates will be in another inertial frame (t',x'^2,x'^2,x'^3).
Now I understand that if have a set of coordinates in one...
Hi, I am a bit confused.
Basically if I have a pdf, fX(x) and i want to work out the distribution of Y=X^2 for example, then this involves me letting Y=X^2, rearranging to get X in terms of Y, substituting these into all values of x in my original pdf fX, and then multipying it by whatever dx...
Hi guys, needing a bit of help understanding laplace transformations.
Homework Statement
1. f(t) = (t-4)u(t-2)
2. g(t) = (2e^-4t)u(t-1)
3. h(t) = 5 cos(2t-1)u(t)
Homework Equations
Laplace transform table.
The Attempt at a Solution
So basically I am given the laplace...
I have a question about mappings that go from a vector space to the dual space, the
notation is quite strange.
A linear functional is just a linear map f : V → F.
The dual space of V is the vector space L(V,F) = (V)*, i.e. the space
of linear functionals, i.e. maps from V to F.
L(V,F)=...
What are the differences in (scalar) field transformations:
1) \phi(x)\to \phi'(x)
2) \phi(x)\to \phi'(x')
3) \phi(x)\to \phi(x')
How this transformations are connected to internal and external symmetries?
For example, if we take spacetime global translations x^{\mu}\to...
what does it mean by "any \Lambda^{\alpha}_{\beta} that can be converted to the idendity \delta^{\alpha}_{\beta} by a continuous variation of parameters must be a proper lorentz transformation"?
Homework Statement
Back in pre-calc, I learned that f(x) can be transformed in the ways of
y = af(bx +c) + d
But very often I come across nastier functions that aren't transformed by scalars, but instead let's say
y = g(x)
what does the transformation do to g(x)?
1. g(x) + x...
Hi, I have a silly question concerning the chain rule. Imagine I have a time and space transformation as follows,
x^0 \rightarrow x^{'0} = x^0 + \xi^0, \ \ \ x^i \rightarrow x^{'i} = R^i_{\ j}(t)x^j + d^i (t) \ \ \ \ \ \ (1)
where xi^0 is constant, R is an element of SO(3) and d is a vector...
I'm a bit lost on this part of my course (ODE's and complex analysis). We've only done about 2-3 of these (seemingly simple) problems where we're given the equation of a line or circle in the complex plane and are asked to find its image in the U-V plane with some transformation \omega, but I...
Hi guys,
I'm currently struggling to show something my lecturer told us in class. We have that
\Psi\left(x\right) \rightarrow S\left(L\right)\Psi\left(L^{-1}x\right)
under a Lorentz transform defined
L = exp\left(\frac{1}{2}\Omega_{ij}M^{ij}\right)
with
S\left(L\right) =...
Identify the Hermite form of the following linear transformations and the basis for its kernel
(x,y,z) = (x-y+2z,2x+y-z,-3x-6y+9z)
So when finding basis for kernel we have to set equal to 0, giving:
x-y+2z=0 (1)
2x+y-z=0 (2)
-3x-6y+9z=0...
I am revising my graph transformations and I am curious:
If we graph sin (2x) or sin (x/2) we are able to increase and reduce their cycles.
Is there any transformation for other lines/graphs?
My doubt is we can also do 2 sin (x), which is the stretch parallel to the y-axis as I am...
Homework Statement Salutations, all. I'm trying to show that if T_A is ergodic, then so is T . This was an iff, and I have the other inplication. I'm a little lost with how to proceed, so any help would be appreciated!
Homework Equations T(X, \mathcal{B}, m) to itself is an...
Hi all, (Also - if anybody could tell me how to get the latex to work on this page that'd be very handy!)
While not technically homework this is a problem I've found I'm stuck on during my revision. Any help would be greatly appreciated.
Homework Statement
"By demanding that the covariant...
This isn't actually a homework problem, but a problem from a book, but as it's quite like a homework problem I thought this forum was probably the best place for it.
Homework Statement
Consider a system with one degree of freedom, described by the Hamiltonian formulation of classical...
Hi :smile:
So: Let f (x) = 3x2 + 6x - 9
For the graph of f:
a) Write down the coordinate of the vertex
b) Write down the equation of the axis of symmetry
c) Write down the the y intercept
iv) Find both x intercepts
My answers:
a) For a I managed to find the x coordinate of the vertex by:
x...
c^2 occurs frequently in special relativity: in the Lorentz transformations, in forumlas for the interval, relativistic energy, and others too. Is there an intuitive reason for the high occurence of c^2?
Homework Statement
My question doesn't require numerical calculation. It is more about explanation.
Here it is: what does it mean to say there are unique linear transformations?
My textbook says "unique linear transformations can be defined by a few values, if the given domain vectors form...
Hello,
Consider the following two situations. There is a train of mass M, going at
V=10 m/s with respect to the train station. There is a mass m passenger
on that train, who starts walking at v=1m/s parallel to the direction of the
train motion. The kinetic energy of this system...
Can someone explain Laplace transformations! i don't understand ittttt.
[edit] sorry. i hadnt even heard of laplace transformations until i found it in my assignment.
basically i want to know how to use them
so, some simple, well explained examples perhaps?
Let L:P1 >> P1 be a linear transformation for which we know that L(t + 1) = 2t + 3 and L(t - 1) = 3t -2
a) Find L(6t-4)
I just want to check the way to calculate this question.
Is L(6t - 4) equal to 6*3t - 4*2 = 18t - 8? if not, how to calculate it?
Homework Statement
Let T : R2 -> R2 be the linear transformation defined by the formula
T(x, y) = (2x + 3y,−x − y).
Let S : R2 -> R2 be the linear transformation whose matrix is
3 −1
2 4
i. Write down the matrix of T.
ii. Calculate the matrices of the linear transformations T o S...
The function of f is given by f(x) = 3x - 2, where x is part of a set of real numbers. Sketch the graph of f. Find a combination of geometrical transformations of which, when applied to the graph of f will give the graph of g(x) = 6x + 1
At a first glance I thought: Stretch by a scale factor...
Homework Statement
Given A =
\left(\begin{array}{ccc}1&-1&1\\0&1&1\end{array}\right)
Why isn't Latex working for above array :(
Define a transformation as
T: \Re^{n} -> \Re^{m}
T(\vec{x}) = A \vec{x}
1)
a. What is n?
b. What is m?
2) Find \vec{x} , if possible, given that...
I'm working my way through Jose and Saletan's mechanics text and I'm at the end of chapter 5 which introduces Hamiltonian dynamics. I've just finished reading about 'types' of generating functions.
They work through an example (5.5) with the following transformation
Q=\frac{m\omega q...
Hi,
So in a general curved spacetime we have no preferred choice of modes and the Bogolubov transformations allow us to convert between the fields expanded in the various complete sets of modes.
If we have one set of modes f_{i} and another g_i both normalized like normalized as...
Two observers A and B are in relative motion with a constant velocity[for example, along the x-x' direction].If A knows the the position of B accurately , the motion of B gets enormously uncertain[and vice verse] in his calculations/considerations.How is he going to derive the Lorentz...
Let us consider the B-E and F-D statics:
{<}{n}_{i}}{>}{=}{\frac{1}{{exp}{(}{{\epsilon}_{i}{-}{\mu}{)}{/}{kT}}{\mp}{1}}
Now we observe the formula from a boosted frame.The left side is a scalar and should not change in response to the Lorentz transformations.What about the right hand side?The...
Hi,
My question is the following. In special relativity, the Lorentz transformations correspond to a physical situation in which two frames of reference move with uniform rectilinear motion one with respect to the other. In general relativity, given the physical situation in which one frame...
Homework Statement
Let V be an n-dimensional vector space over R, and let S and T be linear transformations from V to V.
(i) Show that im(S+T) \subseteq im(S) + im(T)
(ii) Show that r(ST) \leq min(r(S),r(T)), and that n(ST) \leq n(S) + n(T)
Homework Equations
none that i can think...
Homework Statement
A loop moves with velocity v along a charged wire. (The charged wire passes through the center of the loop.)
In a reference frame where the charged wire is stationary and the loop is moving with v, what is the E field and B field at a point on the loop?
In a reference frame...
Homework Statement
if Sa: R2 -> R2 is a rotation by angle a counter-clockwise
if Tb: R2 -> R2 is a reflection in the line that has angle b with + x-axis
Are the below compositions rotations or reflections and what is the angle?
a) Sa ○ Tb
b) Ta ○ Tb
Homework Equations
I don't...
Homework Statement
the mother graph is y = 2 ^ x
Homework Equations
y=2 ^ x
The Attempt at a Solution
so i know the graph is flipped upsidedown and the whole graph is moved up 6 spots
so i can get y = -2 ^ x + 6
however the solutuion is y =-2 ^2x +6.
i can't seem to figure...