Questions tagged [transformation]

Transformation has many meanings in mathematics. If using this tag, add another tag related to the object being transformed. If there is a tag for your specific kind of transformations, use that one instead: e.g., (laplace-transform), (fourier-analysis), (z-transform), (integral-transforms), (rigid-transformations).

Filter by
Sorted by
Tagged with
0 votes
0 answers
10 views

Solving the convolution equation $U*g=\sin{2x}$ where $g(x)=e^{-|x|}$.

The problem is as stated in the title but in more detail: find all tempered distributions $U\in\mathcal{S'(\mathbb{R})}$ that solve the convolution equation given in the title. My approach uses the ...
user avatar
  • 133
0 votes
1 answer
35 views

tanh transformation of symmetric positive definite matrix

Let a symmetric positive definite matrix $\boldsymbol{S}\in\mathbb{R}^{d\times d}$ be given. Consider the following transformation: tanh is applied on the off-diagonal entries and the diagonal entries ...
user avatar
0 votes
0 answers
21 views

Transformation of the histogram

I have two classes in my problem: 'missing' and 'present'. These are the pixel intensities of some pictures. The histogram of their values you can see below. I would like to find some transformation ...
user avatar
  • 113
0 votes
0 answers
12 views

Finding the conjugate/hermitian transpose of a transformation

Hopefully, I'm using the correct terms/names of things, mainly because the language in which I study is not English. Given the operator $T$, in this case is the derivative operator , with the inner ...
user avatar
  • 115
0 votes
1 answer
64 views

How to transform triple integral $\iiint_\Omega \sqrt{1- \frac{x^2}{a^2}- \frac{y^2}{b^2} - \frac{z^2}{c^2} }\ dx dy dz$

I have stumbled across this triple integral $$\iiint_\Omega \sqrt{1- \frac{x^2}{a^2}- \frac{y^2}{b^2} - \frac{z^2}{c^2} }\ dx dy dz$$ where $$\Omega =\left\{(x,y,z)\in{\cal{R}}^3\ \bigg| \ \frac{x^2}{...
user avatar
2 votes
1 answer
55 views

Variance-stabilizing transformation on a simple linear regression

I am currently working with variance-stabilizer method and readed something about it from my textbook. I want to understand it better so I would like to consider a case where I for instance have a ...
user avatar
0 votes
2 answers
25 views

How to properly transform functions?

If $f(x) = \lvert x\rvert$, the graph is this: If $f(2x) = \lvert 2x\rvert$, the graph is this (the blue line). This is as expected. Every point was multiplied by a factor of 1/2: If $f(2x+5) = \lvert ...
user avatar
0 votes
0 answers
15 views

On the Sequence of Transformations of a Function [closed]

I have read the threads on the sequence of transformations of a function and my understanding is that if one changes the order of the transformations, the outcome will change. I tried to test it by ...
user avatar
0 votes
1 answer
25 views

Transformation of derivatives from cartesian to cylindrical coordinates

It is well known that for some function $\phi$ its derivatives have the following relations $$\left[\begin{array}{l} \frac{\partial \phi}{\partial r} \\ \frac{\partial \phi}{\partial \theta} \\ \frac{\...
user avatar
  • 580
3 votes
0 answers
53 views

Undoing radial distortion

I am trying to undo the radial distortion from three known straight lines (in the image projected to arcs due to the radial distortion) as described eg. in http://cv.cs.nthu.edu.tw/upload/activities/...
user avatar
  • 105
2 votes
0 answers
29 views

Showing similarity of triangles

Let be $abc$ and $a'b'c'$ two triangles with same angles, so $ \alpha= \alpha ', \beta= \beta', \gamma= \gamma ' $ I want to show that the triangles are similar to each other by describing a ...
user avatar
0 votes
0 answers
13 views

Convert dataset of discrete changes

Hopefully I'm posting this in the correct community. I'm trying to get my head around this issue. I've got a discrete dataset containing only 'changes'. It will only record a change of state at a ...
user avatar
  • 101
1 vote
1 answer
68 views

How to change coordinates/variables?

I want to model the dynamic behaviour of a point-mass particle moving along a 2D surface given by $h(x_1,x_2)$. I made a question in physics stack exchange, where i found the error in my modelling, ...
user avatar
1 vote
0 answers
31 views

Finding the rotation point given 3 line equations

Edit to better explain the problem: I have 3 sets of points for which I know they are same but rotated about a point (picture a door rotating around a hinge). I emphasized the word "same" ...
user avatar
0 votes
0 answers
22 views

Contravariant Vector Component Transformation from Polar to Cartesian

I am new to tensors and I just learned that the contravarient components of a vector transforms in the following way (using Einstein summation convention) $$A^{'i}=\frac {\partial x^{'i}}{\partial x^j}...
user avatar
0 votes
0 answers
16 views

hessian plane equation basis change with transformation matrix

I've a plane defined in hessian form in 3D by normalized direction (orthogonal vector) (x, y, z) and a signed distance. The distance is signed, because I need to have the option to change plane sides. ...
user avatar
  • 103
-2 votes
0 answers
33 views

Translation of trigonometric function

If you have $7 \cos((\pi/6)(x-3))$ and you want to stretch it by $0.5$ units and then translate it to the right by $3$ units, is the new equation $$7 \cos((\pi/3)(x-4.5))$$ or $$7 \cos((\pi/3)(x-6))$$ ...
user avatar
0 votes
1 answer
19 views

laws of joint distribution of several random variables

How to solve problems of this type? random variables X and Yare independent and have a density $\mathbb{I}_{[0,\infty]}g(x)$. Obtain an explicit formula and plot the density of a random variable $Z=Y/(...
user avatar
0 votes
1 answer
29 views

Demonstrate the inverse tranformation of coordinates (Cartesian Tensors)

I am starting to learn tensors but i'm already stuck in the first question of my problem set, which says: Show that the inverse transformation of $$g'_{i} = \sum_{j=1}^{3} a_{ij} g_{j} $$ is $$ g_{i} ...
user avatar
4 votes
1 answer
92 views

Does the Incomplete Beta function have forms of Elliptic E besides $\frac14 \text B_{\sin^2(2x)}\left(\frac12,\frac34\right)=\text E(x,2)$?

Goal: To find more special cases of the Incomplete Beta function $\text B_z(a,b)$ in terms of Elliptic $\text E(x,k)$ using Mathematica notation: The goal is to find values of: $$\text B_z(a,b)=\int z^...
user avatar
  • 5,209
1 vote
0 answers
81 views

Let $Y\sim F_{\theta}$. When $g(Y, \theta)$ that does not depend on $\theta$?

Let $Y$ be a random vector in $\mathbb{R}^k$, with distribution function belonging to a family $\{F_{\theta}, \theta\in\Theta\}$ is a parametric family of distribuitiuons (e.g. normal with unknown ...
user avatar
0 votes
0 answers
25 views

Fourier transform $u(s,k)=\frac{2\pi \delta(k-1)}{s(ik+s)}$

Let's say I've given the following function $$u(s,k)=\frac{2\pi \delta(k-1)}{s(ik+s)}$$ Where $\delta(k)$ is the Dirac delta function. I would like to find the inverse Fourier transformation of this ...
user avatar
0 votes
0 answers
21 views

Finding another solution of same rotation matrix

I have a Rotation Matrix(3x3)(given) for transforming points in frame A to frame B & I think there can be another Rotation matrix that can give me the same transformation to match the point in ...
user avatar
0 votes
0 answers
36 views

Are there indicators for rads, just like the indicator ° is for degrees?

I am using a formula which calculates an angle $ θ_{h} $, and I am not sure if the result is (as I suspect) rad $\times$ degrees: $$ θ_{h}=\dfrac{π}{2}\sin^{-1}\left(\dfrac{2}{π}-0.2782\right) = \...
user avatar
0 votes
0 answers
42 views

Transformation of integral

I have an integral of the following form $$\int_{-\infty}^{\infty} d\phi_{-2}~\int_{-\infty}^{\infty} d\phi_{-1}~\int_{-\infty}^{\infty} d\phi_{0}~\int_{-\infty}^{\infty} d\phi_{1}~\int_{-\infty}^{\...
user avatar
0 votes
1 answer
22 views

Inverse of a roto-translation matrix in 3D space

I want to create two roto-translation matrices. The first transforms point $P$ into point $P'$ by performing a translation $T=(x_t, y_t, z_t)$ and two rotations (one around the $x$ axis of $\alpha$ ...
user avatar
1 vote
2 answers
38 views

How does synthetic division work for increasing or decreasing the roots of a polynomial equation by a constant factor.

I was browsing previous questions and found the logic behind synthetic division process was explained in Why does synthetic division work? and also browsed the process behind in Purple math website, ...
user avatar
0 votes
1 answer
23 views

how to find transformation matrix of polynomials

I am a student doing my homework. Let $B1 = (1, (t−1), (t−1)^2, (t−1)^3)$ and $B2 = (1, (t+1), (t+1)^2, (t+1)^3)$. How to find a transformation matrix from $B1$ to $B2$? I don't really need an exact ...
user avatar
  • 3
0 votes
1 answer
11 views

Limit Cycle Analysis - State Space Rep. to Polar Coordinates Question

I am trying to follow an example that does not show how a set of dynamics equations is converted to polar coordinates: $\theta=\tan^{-1}\frac{x_2}{x_1}$ $\frac{d}{dt}\tan\theta=(\frac{1}{\cos\theta})^{...
user avatar
0 votes
0 answers
39 views

Transformation of random variable from X to Y

The two random variables $X$ and $Y$ are converted by $Y=g(X)$ as shown in the following equation. Find the probability density function of the random variable $Y$ when the probability density ...
user avatar
1 vote
2 answers
32 views

What formula can transform the table on the left to the table on the right?

I have Table A, which I have to transform into Table B: Table A Table B Difference -8.00 0.00 (+8) -7.00 1.00 (+8) -6.00 2.00 (+8) -5.00 3.00 (+8) -4.00 4.00 (+8) -3.00 3.00 (+6) -2.00 2.00 (+...
user avatar
1 vote
1 answer
29 views

Struggling to follow the transformation from $n \cdot e \left( n-1 \right)\left( \frac{n-1}{e}\right)^{n-1}$

I'm going through the proof in Matousek's discrete maths book and I don't understand how he transforms this: $$n \cdot e \left( n-1 \right)\left( \frac{n-1}{e}\right)^{n-1}$$ to this: $$\left[en \left(...
user avatar
0 votes
1 answer
16 views

Translate a point in 3D according to a distance and an angle

I'm trying to find the coordinates of a point according to this setup: In a 3 dimensional space, I have a point A(xA, yA, zA) and a point B(xB, yB, zB) I would like to get the point C, which would be ...
user avatar
1 vote
1 answer
289 views

Vector in skew coordinate system to cartesian coordinates

I have a skew coordinate system with axes x, y, z’, where x and y are orthogonal to each other. In the third dimension, the z-axis would be the orthogonal axis to x and y, but I don’t have z. Instead, ...
user avatar
0 votes
0 answers
27 views

Equal distribution of transformed random variables

Let $P$ and $Q$ be a pair of distinct continuous probability distributions with densities $p$ and $q$, respectively. Suppose also that we have random variables $X \sim P$ and $Y \sim Q$, and let $Z = \...
user avatar
  • 2,715
0 votes
0 answers
18 views

Marginal density equal to zero everywhere.

I've been working on a two part question on bivariate transformations and marginal densities but am having difficulty finding where I have made a mistake as the final answer for the marginal density ...
user avatar
2 votes
1 answer
39 views

How to locate $O$ if $OA=2OC$?

If you have a segment $[CA]$ and you want to plot the point $O$ such that $(\vec{OC},\vec{OA})=\frac{\pi}{2} (2\pi)$, and $OA=2OC$. How can you plot $O$? From the first condition we know that $O$ ...
user avatar
0 votes
1 answer
64 views

Is $f(x)\cdot g(x)$ a sign-preserving transformation of $f(x)$?

Here are what I learned: a transformation is just a real function $F$. If a real function $f(x)$ is transformed, then $f(x)$ becomes "$F[f(x)]$", which is another real function. Assume $g(x)&...
user avatar
  • 3,006
1 vote
0 answers
41 views

Transformation formula for diferentials

I want to integrate over $\mathbb{R^2}$ and dont know how to proof the change of variables $d\bar{z}dz=2idxdy$ where $z=x+iy$ and $\bar{z}= x-iy$.
user avatar
0 votes
2 answers
30 views

Finding equation whose roots are square of the original but intially some of them were negative .

Consider a cubic given as $x^3 + ax^2 + bx + c = 0$ which has roots $\alpha,-\beta,-\gamma$ , we need to find cubic equation whose roots are $\alpha^2 ,\beta^2 , \gamma^2$ is it possible to get it by ...
user avatar
0 votes
1 answer
42 views

How to transform global coordinates to local coordinates?

For example, I have 4 points with the following global coordinates $(4,2),(5,3),(6,4),(8,5)$. Graph How to transform these global coordinates into local, such that the first point is $(0,0)$ in the ...
user avatar
0 votes
0 answers
21 views

Field transformation upon dilatations

In Lectures on CFT by J. D. Qualls, there appears the following statement without proof (page 30): The scaling dimension $\Delta$ of a field is defined by the action of a scale transformation on the ...
user avatar
  • 499
0 votes
1 answer
21 views

How to transform values from one probability distribution to another

Suppose that I draw randomly the number $0.6$ from the $U \sim \text{Unif}(0, 1)$ distribution. I want to transform this so it follows the distribution of an $Y \sim \exp(\frac 1 2)$ random variable. ...
user avatar
  • 171
0 votes
1 answer
29 views

Coordinate transformation and line element

I am going over a question, for which I know the answer, but I could not figure out how to get to that. I am given the line element $ds^2=dx^2-dy^2=dudv$ and I must find the coordinate transformation $...
user avatar
  • 13
0 votes
1 answer
72 views

An estimation about polynomials in the complex plane [duplicate]

I've been learning complex analysis recently, there's a question about the estimation of polynomials on the real line using the knowledge of complex analysis. Suppose $f(x)={c_0}+{c_1}x+{c_2}x^2+...+{...
user avatar
  • 21
0 votes
0 answers
20 views

Is the Differential Operator Matrix not Isomorphic? If so, why is it not when the derivative is a linear operator?

Is the Derivative operator not isomorphic? I can see by the proof that: D[cx] = cD[x] and D[x + y] = D[y] + D[x] but when I create the map of the derivative of of polynomial space $ \{1, t, t^2, t^3\} ...
user avatar
1 vote
1 answer
45 views

Geometry transformation in function translation

Let $f(x)=x+3$. let's say we want a new function that is a translation of $f(x)$ by $5$ units to the right. If we will denote by $x'$ the new coordinate, Then For all $x$ , $x'=x+5\,\Rightarrow\, x=x'...
user avatar
0 votes
1 answer
71 views

On the Aitchison Geometry

This question is for people who know the Aitchison Geometry - I'm working on a (more mathematical and not statistical) paper on the Aitchison Geometry and I try to understand how ellipses (or any ...
user avatar
  • 337
1 vote
1 answer
28 views

Understanding transformation to Dirichlet distribution to inverted Dirichlet Distribution

This is essentially a question about the paper "On integrals of dirichlet distributions and their applications" by Hedayat Yassaee (1981). Let $K=\frac{\prod_{i=1}^{k+1}\Gamma(v_i)}{\Gamma(\...
user avatar
  • 738
0 votes
0 answers
2 views

Can Transformation of Continuous Random Variables be used to explain a transformation of CDF Probabilities?

I am reading a technical paper that states the following (also see image link below for CDF PROBLEM illustration): CDF of X at (x) = CDF of Y at h(x) can be written as: h(x) = Inv_CDF of Y at CDF of X ...
user avatar

1
2 3 4 5
55