# 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).

738 questions
168 views

### Transformations of RV's Ensuring Absolute Continuity of Quantile Functions

Given a real random variable $X$, suppose $T:\mathbb{R}\to\mathbb{R}$ is non-decreasing. Define $Y=T\left(X\right)$. Let $Q_{X}$, $Q_{Y}$ be the corresponding right-continuous quantile functions. ...
573 views

### Way to Tietze's Transformation Theorem

During our knot-theory lecture we have talking about the following theorem: Given two finite presentations of the same group, one can be obtained from the other by a finite sequence of Tietze ...
50 views

### Certain symmetrized product of cosines - can it be transformed into more manageable form

I am interested in the following expression: $$F_{k_1,\ldots,k_n}(t):=\sum_{\sigma\in S_n}\cos(\sigma(1)k_1t)\cos(\sigma(2)k_2t)\cdots\cos(\sigma(n)k_nt)$$ where $k_1, \ldots, k_n$ are natural ...
142 views

428 views

### How to use polynomial or conformal transformation

In my research, I came to a transformation problem. The simple version is an initial circle (or sphere) region is advected by some deformational flow. After some time the circle will be deformed into ...
54 views

139 views

### Changing coordinate system with non standard definitions

The standard coordinate transformation to polar coordinates is $$\begin{cases} x=r\cos(\varphi)\\ y=r\sin(\varphi) \end{cases}$$ with $r\in[0,\infty), \ \varphi\in[0,2\pi)$ The question is whether I ...
194 views

### Proof for a summation-procedure using the matrix of Eulerian numbers?

I've discussed a procedure for divergent summation using the matrix of Eulerian numbers occasionally in the last years (initially here, and here in MSE and MO but not in that generality and thus(?) ...
22 views

37 views

### Does, under iteration, all strongly mixing transformations tend to spread sets out, not only in (ordinary) diameter, but also in harmonic diameter?

In [R. E. Rice, On mixing transformations, Aequationes Math. 17 (1978), 104 – 108; Theorem 2 (motivated by some physical phenomena and offer some clarifications of these phenomena)] it is shown that, ...
112 views

### how to transform ellipse back to circle

I have a circle in a $xz$ plane with its center at Origin $O$ as shown in the diagram. The circle is being observed by a camera from point $C$ at $yz$ plane at an angle $\beta$ with the $z-$ Axis. ...
132 views

94 views

### How do I draw this picture in squares of discrete $\sqrt{z}$?

From Richard Kenyon's homepage gallery: I want to understand the mathematics of this, and similar/related transformations. ... An explanation in words (1st year uni level maths) would be ideal. I'...
372 views

### Proving non-linear mapping is invertible using partial derivatives only

Given $f : \mathbb{R} \rightarrow \mathbb{R}$, it's possible to show that $f$ is a bijection by considering its derivatives only: if the derivative is always positive or always negative, then the ...
251 views

### Angle by which tangents to curves at $z_{0}$ are rotated under the mapping $w = z^{2}$

I have to find an angle by which tangents to curves at $z_{0}$ are rotated under the mapping $w = z^{2}$ if (a) $z_{0} = i$, (b) $z_{0} = -1/4$, (c) $z_{0} = 1+i$, and also find the corresponding ...
332 views

### Perspective correction from 3 points and foreshortening factor

I'm working on creating a homography 3x3 matrix to do a perspective correction of a photograph 2D piece of paper. The paper contains 3 markers (like the 3 corner markers of a QR code) in its corners, ...
119 views

### How to determine changing scale factors when performing coordinate transfomations?

To explain: I have two coordinate systems. One $(x,y)$ and the other $(x',y')$ as seen in this diagram. Coordinate systems I am trying to convert the coordinate in the $(x,y)$ system to the rotated ...
53 views

### Distribution of discrete function of continuous random variable?

It has been quite some time that I did statistics, and I am not sure how to figure out the distribution of a function of a random variable if the function itself discretizes (if that is a word) the ...
347 views

### Fourier Transform of triangle function

I have a question regarding the FT of the triangular function: How does $e^{-j\omega t}$ becomes the cosine function in the first line? What happened to the sine when you go from $e^{j \omega t}$ ...
78 views

### Change from Fourier Space to Real Space

I have a function in 3D fourier Space $$g(\textbf {k})=\frac{\hat{k}_i}{\hat{k_j}}f(\textbf {k}),$$ where $\hat{\alpha}$ is a fixed vector and $i$ and $j$ are the components of the relevant vector, ...
37 views

### What is the name of this transformation's property?

I have a transformation $P$ with the following property: $P^n = \mathbb{I}$ (the identity) for some specific $n>1$, and all $P^m \neq 1$ for $m \neq n$. What is the name of the property of $P$? ...
26 views

### What does the s-Transform (exponential transform) mean conceptually? What does it show us?

I don't understand the conceptual idea. If I have PDF, and I calculate its s-transform for some s, what do I know that I did not know before?
157 views

### Compare between Short Time Fourier Transform and Wavelets

Fourier transform is localised in only frequency domain but Short time Fourier transform(STFT) is localised both in time and frequency domain same as in wavelets. I want to know How are STFT and ...
147 views

### Finding the transformation matrix of a projective transformation in RP^2

So I want to understand how to find the matrix that represents the projective transformation that sends 4 given points to 4 given images, I know that 4 points are necessary to determine it but I can't ...
57 views

### Find a matrix to represent the mapping of a factor module

I have a problem from my past paper I can't figure the logic to, even after seeing the answers. The question goes 【Q】Let $V=\mathbb{R}[X]_{<4}$ be the vector space of real polynomials of degree ...
45 views

### The Adrian Transformation of a function in $\mathbb{R}^{2}$

Recently I came upon a problem (if you would call it that, more of a thought experiment), which was phrased something like this: Rotate the area formed by $\int_{-1}^12dx$ around the curve \$h(x)=-x^...