# transformation

1. ### Transformation notation question

I taught middle school math and I'm somewhat familiar with transformations, but I have no idea what the notations in this problem mean. I looked in two geometry books with no luck. Google, no luck. Khan Academy, well, you get the idea. I'm tutoring two students who are doing distance...
2. ### Legendre Transformation

First, we begin with a definition. Definition: Let $f:A\to \mathbb{R}$ be a function defined on a subset $A\subseteq \mathbb{R}^k$. The Legendre transform $f^*$ of $f$ is defined by $$f^*(p)=\sup\{x\cdot p-f(x)\mid x\in A\}$$ for all $p\in \mathbb{R}^k$ where this supremum on the right-hand...
3. ### Doubt about Linear transformation

Hi (excuse me about my english). I have a doubt about this linear transformation: f(x) = x - 1 There is a theorem that says that if the kernel of the transformation is 0; then the transformation is inyective: if the ker (f(x)) = 0 But in this linear transformation the ker (f) = { x = 1 } ...
4. ### Function tranformation

Hi, I hope someone can help. I'm doing question 7a. I'm trying to understand why the x-value for 7a is -2 as opposed to -3. I thought that you always applied reflections before translations, so I'm confused why this case is different. Please help :)
5. ### Transformation of a polynomial function

Hi, I hope someone can help. So I developed a polynomial function: f(x) = 1/9(x+3)(x+1)(x-3)(x-1) I am now trying to horizontally compress this function by a factor of 2. Can someone please confirm with me that the new equation with this transformation applied is f(x) =...
6. ### A simple question: can a linear transformation have the same matrix in different base

Hi: can a linear transformation have the same matrix in different bases? I have spent a whole evening trying to figure out whether this can be to no use. What is certain is that given a base, I can define a linear ttransformation by giving it's values over a base. That is, there exists a...
7. ### Special Relativity - Lorentz Transformation

Hi, I am not sure if I am posting under correct thread. I am wondering if anyone could help me out with the following suppose a Photon travels from One event E1 with co-ordinates (t1, x1) to another event E2 with co-ordinates (t2,x2). Show that under the Lorentz transformations the speed of the...

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9. ### Metric transformation

I'm trying to understand the paper by Hitchin called ''Polygons and gravitons", Polygons and gravitons - INSPIRE-HEP. I'm stuck at page 471. At this point, he does some computations and obtains a metric: \gamma dz d\bar{z}+\gamma^{-1}\left(\dfrac{2dy}{y}+\bar{\delta}dz...
10. ### Girsanov transformation

Hello, I would like to use the Girsanov transformation in the Black-Scholes model with infinite time horizon in order to find an equivalent martingale measure. The problem is not the Girsanov transformation itself but the existence of the probability measure. Here is a more detailed...
11. ### Girsanov transformation in the Black-Scholes Modell with infinite time horizon

Hello, I would like to use the Girsanov transformation in the Black-Scholes model with infinite time horizon in order to find an equivalent martingale measure. The problem is not the Girsanov transformation itself but the existence of the probability measure. Here is a more detailed...
12. ### Discrete Cosine Transformation

Hi all, I'm an undergrad from brazil. While I was fumbing around with a C++ implementation of DCT (discrete cosine transform - II : https://en.wikipedia.org/wiki/Discrete_cosine_transform#DCT-II) I stumbled upon something: DCT(X) * DCT(Y) = A* X*Y where X and Y are vectors. Let me demonstrate...
13. ### Linear Transformation Question

Hi, I need to write the matrix that represents the following linear transformation of the plane and then draw the image in quadrant 1. ...The transformation T(x,y)=(2x+6y, x+3y) The matrix I got was: 2 6 1 3 This led to reference points: O(0,0) - O'(0,0) P(1,0) - P'(2,1) Q(1,1) -...
14. ### Prove that the Transformation is Self Adjoint

Let $T$ be a normal transformation - $TT^*=T^*T$, where * is the self-ad joint operator in a finite space. Prove that if $T^3=\frac{1}{2}(T+T^*)$, then T is self adjoint. I have tried to do some math on $(Tv,u)$ but I was not successful in proving the following: $(Tu,v)=(u,Tv)$ which is what I...
15. ### Similarity transformation

I'm trying to find a similarity transform (obviously) that has the following properties: S^{-1} ~ \left ( \begin{matrix} 0 & 0 & z & x - iy \\ 0 & 0 & x + iy & -z \\ z & x - iy & 0 & 0 \\ x + iy & -z & 0 & 0 \end{matrix} \right ) ~ S = \left ( \begin{matrix} 0 & 0 & -i & 0 \\ 0 & 0 & 0 & -i \\i...
16. ### Matching moments of distributions of a random variable x and a transformation x1=x^2

My statistics have become a bit rusty. I am puzzled with a problem. Let assume that x is a random variable and can either x ~ Normal(0,1) or x ~ Uniform(a,b) From Normal : E(x) = 0, V(x) = 1 From Uniform : E(x) = 1 / (a+b), V(x) = 12 / ( (b-a)^(2) ) If we want to match the mean and the...
17. ### Unitary transformation in commutator expansion

I would like a proof or an outline of one for the following identity: exp(A)*B*exp(-A) = B + [A,B] / 1! + [A,[A,B]] / 2! + ... + [A,[A,...,[A,B]...] / n! + .... A and B are linear operators in the case I am considering, but the identity is a formal one, which I believe depends only on the...
18. ### Complex transformation

'A transformation from the z-plane to the w-plane is given by $w=\Large\frac{z-\text {i}}{z}$ Show that under this transformation the line Im(z) = $\large\frac{1}{2}$ is mapped to the circle with equation |w| = 1. Hence, or otherwise, find in the form $w=\Large\frac{az+b}{cz+d}$ where \$a, b...
19. ### coordinate transformation

I have the coordinates of four points on a plane. This figure has been rotated, translated, and scaled and I have the coordinates of the corresponding transformed points. What I need to be able to do is determine the transformations so that I can apply them to another point in the original...
20. ### Hello and help with Transformation / solving for Vn

hello, I'm new here and having an issue figuring out how to rearrange the following equation. Sorry again, but I messed up in the title. Its not transformation, but tranposition or rearranging to solve for Vn. Thanks