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).
883
questions with no upvoted or accepted answers
2
votes
2
answers
238
views
Integration similaring to Fourier transform of Gaussian function
I would like to calculate the integral:
$$\int^{\infty}_{0}x\cdot \exp(-x^2)\cdot \exp(-ikx)dx$$
Are there some tricks to solve it?
Many thanks.
- 63
2
votes
0
answers
485
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, ...
- 121
2
votes
0
answers
390
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 ...
- 21
2
votes
0
answers
72
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 ...
- 121
2
votes
0
answers
920
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 $e^{j \omega t}$ ...
- 157
2
votes
0
answers
326
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, ...
- 497
2
votes
0
answers
43
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 $P$? ...
- 924
2
votes
0
answers
31
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?
- 166
2
votes
0
answers
209
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 ...
- 534
2
votes
0
answers
382
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 ...
- 159
2
votes
0
answers
77
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 ...
- 567
2
votes
0
answers
47
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^...
- 3,948
2
votes
0
answers
1k
views
Solids of Revolution around other functions.
Recently I've been thinking about solids of revlution, and thought about an interesting experiment. Can you rotate functions around, for example, the line $f(x)=x$? And consequently, could you rotate ...
- 3,948
2
votes
0
answers
252
views
The Composition of Two rotations
So far I rewrote the halfturns of d,c,b,a to halfturn (p,n)(m,l) where n=m because lines c and d are parallel so I can make ambiguous lines n and p parallel too. I also know that lines c,d can be ...
- 21
2
votes
0
answers
88
views
When creating conformal images, how do you change the basis of the input lattice such that spirals result in the transformed image?
I am trying to emulate the results shown in the Wikipedia page on Conformal Images in an attempt to better visualize complex functions (and stare at some trippy images, man). The script I wrote (...
- 21
2
votes
1
answer
831
views
Hyperbolic Geometry: Question about the Transitivity of Möbius transformations
I was confronted with this exercise in the book Hyperbolic Geometry by Anderson which states:
In each case, find $m \in Möb(\mathbb{H})$ such that the property holds, or prove that no such $m$ ...
- 21
2
votes
0
answers
163
views
Transforming the cubic Pell-type equation for the tribonacci numbers
The Lucas and Fibonacci numbers solve the Pell equation,
$$L_n^2-5F_n^2=4(-1)^n\tag1$$
The tribonacci numbers $z = T_n$ are positive integer solutions to the cubic Pell-type equation,
$$27 x^3 - 36 x ...
- 54.6k
2
votes
0
answers
222
views
Is there an interesting interpretation of the ROWS of an affine transform matrix?
Context: I have a question about affine transform matrices in 3-space. Matrices are 4x4, with the right-most column being the translation, and the bottom row being [0,0,0,1].
In discussions I read ...
- 139
2
votes
1
answer
170
views
Transformation of a Random Variable
We have a random variable $x$ with p.d.f. $\sqrt{\dfrac{\theta}{\pi x}}\exp(-x\theta)$, $x>0$ and $\theta$ a positive parameter.
We are required to show that $2\theta x$ has a $\chi^2$ ...
- 21
2
votes
0
answers
30
views
Finding the matrix ${\left[ T \right]_E}$
Let the matrix ${\left[ T \right]_{B \to E}}$, the matrix where:
$${\left[ T \right]_{B \to E}}{\left[ v \right]_E} = {\left[ {T(v)} \right]_B}$$
It's given that:
$${\left[ T \right]_{B \to E}} = \...
- 2,920
2
votes
0
answers
106
views
Finding transformation from $T : \Bbb R^5 \rightarrow \Bbb R^4 $ ...
Is there a Linear Transformation from $T : \Bbb R^5 \rightarrow \Bbb R^4 $ so $$\operatorname{Ker}T = \{(
x,y,z,t,w) \in \Bbb R^5 \; | \; x = 2y, \text{ and, } z = 2t = 3w\}$$
if so find an example of ...
- 672
2
votes
0
answers
58
views
Manipulating this probability distribution function
I have a probability distribution function as follows:
$$
P(y|x,w, \phi) = \frac{\phi}{2\pi} \exp ^{-0.5 (y-t(x, w)'\phi (y-t(x,w)) }
$$
Here $y$ and $x$ are two observed values. $\phi$ is also some ...
- 513
2
votes
0
answers
681
views
Algorithm to determine matrix equivalence
I'm a physicist who's not particularly good at linear algebra so please accept my apologies if this is standard textbook stuff that I'm just unaware of.
I have two real rectangular matrices $A_{mxn} ...
- 131
2
votes
0
answers
367
views
Get 2D coordinate transformation matrix based on points in a system and their angles in the other?
I'd like to get the parameters (rotation angle,$\Theta$, and translation coefficients, $x_0$ and $y_0$)) of a transformation for translating and rotating points in a coordinate system to another. As ...
- 21
2
votes
2
answers
828
views
For general non-symmetric square matrices is there a matrix norm that is invariant under similarity transformations?
I think that there is no similarity-invariant matrix norm for general matrices. But are there similarity invariant norms for special types of matrices (e.g. for matrices whose eigevalues are different ...
- 21
2
votes
0
answers
135
views
Transformed Laplace "solution space"
From my own knowledge I can tell that when we take the Laplace transformation of a function we are in essence transforming our f(t) into a F(s).
I've looked at several Q/A here asking for the ...
- 165
2
votes
0
answers
160
views
Stabilize Variance for Statistics (Transformation)
Problem: When $Y (> 0)$ has mean and variance equal to $\mu$ and
$\mu/n$ respectively, it is shown in the textbook that the appropriate transformation of Y to stabilize variance is the square root ...
- 41
2
votes
0
answers
49
views
Inverting a discrete linear transformation
Consider the transformation from the set $\{a_n\}_{n=0}^N$ to the set $\{p_j\}_{j=0}^N$: $$ p_j = \sum_{n = 0}^Na_n\phi_n(x_j)$$ where $\{\phi_n(x)\}_{n=0}^N$ is a set of basis functions (linearly ...
- 1,729
2
votes
0
answers
114
views
Following a polyline along the surface of a polygon that is twisted
I have (hopefully) an interesting problem regarding geometry. I will also search online and in literature but I thought to pose the question here as a third resource.
For my problem I need to get the ...
- 159
2
votes
1
answer
218
views
Is there an intuitive understanding of what a walsh coefficient is?
I am working with Walsh coefficients.
I know the intuitive understanding is almost that that they are the degree of connectivity, but it is there a better way of thinking about it? What is the ...
- 1,047
2
votes
0
answers
206
views
bound on Hilbert transform
Consider $\widehat{Tf(\xi)}=m(\xi)\hat{f}(\xi)$, where $m(\xi)=(1-\vert\xi\vert)1_{[-1,1]}$, i.e. $T$ is the operation of taking Fourier transform and multiplying with the function $m(\xi)$. I am ...
user48603
2
votes
0
answers
562
views
Understanding Discrete Cosine Transformation
I'm currently working on some software and a key component is 2D DCT. But my question is more general, as I'm trying to understand the DCT in general, let's say from engineers point of view.
For start,...
- 133
2
votes
0
answers
252
views
transformation of coordinate systems by rotation
I am trying to convert a set of coordinates from ECEF (Earth Center Earth Fixed) to ENU (East North Up). The operation is performed by applying a rotation matrix as shown in:
[http://en.wikipedia.org/...
- 21
2
votes
0
answers
208
views
Transform 3D vectors between planes using a matrix
I've got 6 points in 3D space: $A,B,C,D,E,F$, that represent 4 vectors. $AB$ is perpendicular to $AC$ and $DE$ is perpendicular to $DF$.
I need to find a transformation matrix M, that transforms $AB$ ...
- 21
2
votes
0
answers
2k
views
How to project a spherical map onto a sphere / cube
I have this panorama, an spherical map from google streetview, and want to map this on a sphere/cube. Below are some examples and illustrations, i am going to implement it in c++ and are not sure ...
- 163
2
votes
0
answers
836
views
Joint distribution of transformed variables
I have a problem in deriving the transformed joint distribution for continuous random variables. The textbook says use jacobian which makes sense but I wanted to go from first principles like below... ...
- 181
2
votes
0
answers
189
views
Hyperbolic Universal Covering Space
I have been working with Ricci flow in the euclidean and hyperbolic space but have been having considerable trouble determining how to generate a universal covering space for complex hyperbolic meshes....
- 31
2
votes
0
answers
974
views
How to find the center of an (scaled) ellipse?
This question is an extension of How to find the center of an ellipse?.
The solution there works well, but in Javascript the floating point calculations are not that accurate. The workaround is to "...
- 257
2
votes
2
answers
151
views
Transforming a weighted sum to another one with different weights
Let $x_1, x_2, \dots, x_n$ and $w_1, w_2, \dots, w_n$ be real numbers and $f_1 = x_1+\dots+x_n$ and $f_2 = w_1x_1+\dots+w_nx_n$. Is it possible to find a transformation $T$ which $T(f_1)=f_2$.
- 338
1
vote
1
answer
42
views
+200
A domain-covariant notation for functions?
Note: I'm using the terms "covariant" and "contravariant" a bit loosely in this question.
The standard function notation seems to be naturally codomain-covariant and domain-...
- 3,822
1
vote
0
answers
66
views
converting pose (which is a quaternion & a vector) from a coordinate system to another
The question is about a world and a camera that is defined in this world. I want to transform the pose (which is a rotation and a translation) of the camera given in the world coordinate system (...
- 11
1
vote
0
answers
38
views
Inverse transform of a sine kernel
I’m not a mathematician and I’m working with some transforms in physical chemistry.
I use a transform to pass from the time domain of phase domain in a process that use a square wave to perturb and ...
- 21
1
vote
0
answers
81
views
Is it possible to split the optimization problem into multiple sub problem if the objective function and constraints are separable?
I am a post graduate electrical engineering student who is working with some optimization. Suddenly, I realize that my problem ${\left( P \right)}$ is quite separable in both objective function and ...
1
vote
0
answers
102
views
Finding the inverse of a matrix using elementary transformations
$$A:=\begin{pmatrix}
1 & 2 & 3
\\\\ 1 & 3 & 5
\\\\ 1 & 5 & 12
\end{pmatrix}$$
Using $A = A I$ where left hand side is transformed into an identity matrix using ...
- 11
1
vote
0
answers
49
views
Can a triangle $ABC$ be translated onto another triangle $PQR$ in multiple ways?
For example, if $ABC = (0,1), (2, 3), (4, 7)$ and $PQR = (-1, -1), (1, 1), (3, 5)$, then the only way $ABC$ can be superimposed onto $PQR$ is by a translation $1$ unit left and $2$ units down. This ...
- 1,940
1
vote
0
answers
70
views
Show that there is a Lipschitz-continous function $f:[0,1]\rightarrow[0,1]$ for that $f(A)=[0,b]$ ($0<b\leq 1$ and $A\subseteq[0,1]$)
I am working on the following task:
Let $A\subseteq[0,1]$ Lebesgue measureable with $\lambda^1(A)>0$. Show that there is a Lipschitz-continous function $f:[0,1]\rightarrow[0,1]$ and $0<b\leq1$ ...
1
vote
0
answers
45
views
Transformation of Random variables on MGF
Assume $X$ a continuous non-negative random variable follow a Gamma distribution having shape parameter $k$ and scale parameter $\theta$ with the following CDF
\begin{align}
F_{X}(x) =\frac{\gamma\...
1
vote
0
answers
36
views
$M/G/\infty$: application of marking and transformation, finding the mean measure
Consider a queue $M/G/\infty$, starting with arrival time of calls as a PPP$(\Lambda)$ and lengths of calls as $iid$ random variables with common distribution $G$. The times when the calls terminate ...
- 2,146
1
vote
0
answers
78
views
What is the most general mathematical definition of symmetry?
I have heard of definitions along the line of saying that a transformation T of something with respect to a certain property p is symmetric if, after T is applied, p remains unchanged. Is there a way ...
- 1,121
1
vote
0
answers
7
views
ensemble overlap after transformation
I have 2 ensemble for which i would like to mesure their similarity/overlap, but there is no existing method to do this on the type of data contained in these ensemble.
However i can apply a ...
