# 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).

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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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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 $$\Omega =\left\{(x,y,z)\in{\cal{R}}^3\ \bigg| \ \frac{x^2}{... 2 votes 1 answer 55 views ### Variance-stabilizing transformation on a simple linear regression I am currently working with variance-stabilizer method and readed something about it from my textbook. I want to understand it better so I would like to consider a case where I for instance have a ... • 304 0 votes 2 answers 25 views ### How to properly transform functions? If f(x) = \lvert x\rvert, the graph is this: If f(2x) = \lvert 2x\rvert, the graph is this (the blue line). This is as expected. Every point was multiplied by a factor of 1/2: If f(2x+5) = \lvert ... 0 votes 0 answers 15 views ### On the Sequence of Transformations of a Function [closed] I have read the threads on the sequence of transformations of a function and my understanding is that if one changes the order of the transformations, the outcome will change. I tried to test it by ... 0 votes 1 answer 25 views ### Transformation of derivatives from cartesian to cylindrical coordinates It is well known that for some function \phi its derivatives have the following relations$$\left[\begin{array}{l} \frac{\partial \phi}{\partial r} \\ \frac{\partial \phi}{\partial \theta} \\ \frac{\...
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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/...
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### 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 ...
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### 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 ...
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### 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, ...
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### 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" ...
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### 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 ...
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### 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, ...
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### 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 $\bar{z}= x-iy$.
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### 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 ...
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### 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 ...
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### 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 ...
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### 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. ...
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### 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 ...
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