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-...

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Extracting sign of scaling from modelView matrix

I want to retrieve the sign of scaling for each axis from modelview matrix. Right now I am able to extract the sign only if all 3 signs are same but it fails when one of them is different. Here is the ...
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1answer
18 views

Transformation of functions: proof for the time period

Given the standard form of a trigonometric function: $a \times \cos(b(t+c)) + d$, what is the proof that the period $p = \frac{2 \times \pi}{b}$. We don't have the proof in our syllabus. I'm just ...
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18 views

Determine a change of variables to transform one DE to another

Given two ODE's, is it possible to determine if one can be obtained from the other via a change of variables? In particular, I have the two ODEs: $$ \begin{split} \frac{d^2y}{dt^2}&=\frac{8t-3}{...
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2answers
18 views

Find coordinates of intersection

The question says "The line with equation $y = - \sqrt{3}$ intersects the graph at points A and B, find coordinates of point B." I worked out that the graph formula is $y = 2\cos(2x)$ and I think I'm ...
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1answer
12 views

Can a boolean value concerning changing the sign or not of a scalar value considered a 1D rotation?

So going descending order on dimensions: 3D: 3 scaling scalars, 3 rotation scalars, 3 translation scalars 2D: 2 scaling scalars, 1 rotation scalars, 2 translation scalars 1D: 1 scaling scalar, 1 ...
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2answers
41 views

How to transform a 2-d space on a circle to a higher dimension space

I have 2 points $A=(x_A,y_A), B=(x_B,y_B)$ on a unit circle $O$. The distance between $A$ and $B$ goes through the perimeter of the circle. How can I transform this space to a space with higher ...
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0answers
28 views

Exponential to Weibull Distribution transformation

Let X~Exp($\lambda$) and let Y=$\lambda$$X^{1/\gamma}$. Find and name the distribution Y. So considering the CDF of Y, I have that $F_Y(y)=1-e^{-\lambda(y/\lambda)^\gamma}$. This is looking very ...
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0answers
8 views

Exponential Distribution Transformaion

Let X~Exp($\lambda$) and let Y=$\lambda$$X^{1/\gamma}$. Find and name the distribution Y. So considering the CDF of Y, I have that $F_Y(y)=1-e^{-\lambda(y/\lambda)^\gamma}$. Now I think the next ...
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1answer
58 views

Mapping from the z-plane to the w-plane

I'm struggling with this question Show that the transformation w=z-1/z maps |z-1|=1 in the z-plane to |w|=|w-1| in the w-plane. Any help would be much appreciated. Thanks
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1answer
93 views

A Lipschitz transform maps measurable set to measurable

Prove that a Lipschitz transform $T: \mathbb{R}^n \to \mathbb{R}^n$ maps measurable set to measurable. Assume the only thing that we know about Lipschitz transform is that we can find $M>0$ such ...
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1answer
37 views

How do I solve this complex numbers problem: transformation from the z plane to the w plane?

The point $P$ represents a variable point $z = x + iy$ in an Argand diagram. The point $Q$ represents a variable point $w = u + iv$ in a second Argand diagram and $x$, $y$, $u$ and $v$ are real ...
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18 views

Linear transformations that preserve permutations of a vector.

Forgive me if this question sounds silly. Let $v$ be a $m \times 1$ vector and $P$ be a $m \times m$ permutation matrix. Can there be a transformation $T$ such that $\min_\limits{P\neq I}\|Tv-TPv\|$ ...
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1answer
28 views

How to solve this graphical function transfromation problem?

How to solve problems like this. I always face problem in solving function transformation related problems. Is there any good way to solve problems like this..
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2answers
22 views

Triple integration, Spherical coordinates

How do we get limit such as $0\le\theta\le\pi$, $0\le\phi\le2\pi$ in spherical coordinate system where $$x=r \sin\theta\cos\phi, y=r \sin\theta\sin\phi, z=r \cos\theta$$ Why is the $\theta$-limit $[0,...
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0answers
15 views

Similarity between two 2-D Transforms

How can I measure the similarity between two 2-D transforms? For instance, I would like to find how much similar is the 4x4 Hadamard Transform (H) with the 4x4 integer DCT (D), as used in H.264/AVC (a ...
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1answer
218 views

A linear transform of a closed set is closed

A linear transform of a closed set $E\subset \mathbb{R}^d \to \mathbb{R}^d$ is closed. I have seen a lot of similar questions here, but none of them exactly addresses the issue. Please if you find ...
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36 views

Can the z-transform/laplace transform be generalized?

The fourier transform is a special case of z/laplace where the countour being projected on is the unit circle. The ztransform/laplace transform then generalizes this to a circle of any radius. Is ...
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2answers
30 views

transformation of differential equation

1.$$ x^2(1+u)dx + x^3(1-u)du = 0 $$ 2.$$ \frac {1-u}{1+u}du + \frac {dx}{x} = 0 $$ I know from 1 to 2 the equation is divided by $x^3(1+u)$, but i don't understand how that happens,was reading ...
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1answer
34 views

Corresponding matrix field basis

Hi people, I'm reviewing my notes for an exams and this is a question which I was unable to wrap my head around for many months. It should be fairly simple but I might be lacking a crucial piece of ...
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1answer
29 views

Is there a concise, specific name for a transform that consists of rotate, scale and translate?

I'm working on software that involves transforming between different mapping coordinate systems. In one part of the maths/logic, I have to derive, then apply a transform between two cartesian ...
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0answers
32 views

Tranformation of random variables

Let $X$ have the p.d.f $f(x)= e^{-x}$, $ x > 0$, $0 $ otherwise,find the pdf of $Y = X^2$ and space range $Y$. I use the change of variable formula The inverse is $${x} = \sqrt{{y}} $$ The ...
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1answer
19 views

What is this method of scaling called? Can it be generalised?

Consider the problem of finding the values of $\alpha_1, \alpha_2, ..., \alpha_k$, subject to constraints, such that the following equation is satisfied \begin{equation} \alpha_1 x_1 + \alpha_2 x_2 + ...
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0answers
28 views

fourier transform of a function that is only partially known

I'm interested in periodicity of a function that is not known completely, one way to think about it: our function $x(t)$ is defined at discrete points $t_1, t_2, ...$ but the values at these points ...
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63 views

Find me a sigmoid function with fixed point at the point of inflection in the unit interval

I am interested in finding sigmoid (S-shaped) functions $f$ on the unit interval $[0,1]$ such that For some $a \in (0, 1)$, $f(a) = a$ and $f'(a^-) > 0$ and $f'(a^+) < 0$. $f(0) = 0$ and $f(1) ...
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2answers
27 views

Before and after a transformation apply another transformation and its inverse?

So I have something like $y(x) = x\cdot5$, so whatever $x$ is, it's being scaled up by $5$. But I could center that scaling to a different point reference other than $0$. For example $10$. So for ...
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1answer
14 views

Method for transforming one curve around another?

I'm working with a complex problem involving waveforms. Essentially I want to bend a given waveform around a circle. At it's most basic, I want to take one curve on a linear graph and map it onto a ...
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1answer
13 views

Z transformation with $k$ from non-zero

we known that $Z$ transformation of $f_k$ is defined as $$F(z)=\sum_{k=0}^{\infty}f_k z^k$$ My problem is if $k$ starts from $m$, where $m >0$, then $\sum_{k=m}^{\infty}f_{k+m} z^{k+m}$ is still ...
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119 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. ...
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74 views

Best sources on complete transforms (classic orthonormal transforms) and overcomplete transforms in signal processing

In the introduction section of a thesis I read a little about classic orthonormal transforms such as Fourier, discrete cosine and wavelet transforms and their application in signal processing. Then ...
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25 views

Transformations of discrete random variable

I understand how to do transformations. Well, I thought I did. But I can't seem to comprehend how to do a discrete to discrete. Here is the question I am working with. (I am currently studying for an ...
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5answers
34 views

f(2x + 1) transformation

I was working on a problem that asked: If there is a vertical asymptote at $x = 5$ for $f(x)$, where is the vertical asymptote for $f(2x + 1)$? The correct answer is at $x = 2$, but this ...
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1answer
114 views

Linear Transformations finding matrix in respect to a basis and coordinate change matrix.

Define $T: Poly_2 \ to\ Poly_2$ by $$T(at^2+bt+c)=3ct^2 +2at-b$$ 1) Show that T is a linear transformation and give a matrix A for T with respect to the basis $B=\{t^2,t,1\}$. 2) Give a ...
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1answer
37 views

Find Fourier transform of triangular function based on a Fourier results of rectangular

I have a triangular pulse given by $$x\left(\frac{t}T\right) = \begin{cases} 1-\frac {|t|}T, & \text{if $T\ge t$} \\ 0, & \text{otherwise} \end{cases}$$ Given that $F\left(\operatorname{rect}...
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1answer
59 views

Order of Operations for Horizontal Transformations

We know that when we want to combine two horizontal transformations, specifically that of translating and stretching a function, we have to translate $f(x)$ first, and then afterwards stretch it. ...
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1answer
48 views

PDF for $\frac1a Uniform(−a,a)$

Problem: Let $X$ be $Uniform(−a,a)$ distrubuted. Calculate the PDF for $Z = \frac1a abs(X)$. Attempt: I think graphically here. $X$ is $U(-a,a)$ with $PDF = \frac1{2a}$ so $abs(X)$ is $U(0,a)$ with $...
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1answer
121 views

Show random variables are mutually independent

Let $X_1$,$X_2$, $X_3$ denote a random sample from the distribution having p.d.f $$f(x) = e^{-x},\,\, 0<x <\infty,$$ zero elsewhere. Show that $$y_1 = \frac{x_1}{x_1 + x_2} $$ $$y_2 = \frac{...
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1answer
78 views

Mellin transform of Gumbel distribution

The probability density function (PDF) of Gumbel distribution is given as: $$f\left(x\right)=\frac{\exp \left(-\left(\exp \left(-\frac{x-\mu}{\beta }\right)+\frac{x-\mu}{\beta }\right)\right)}{\beta }...
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2answers
51 views

Using the dimension formula to prove isomorphism

Let V be a finite-dimensional vector space and $T: V\rightarrow V $. T is a linear transformation. Use the dimension formula to prove that if T is injective, it must also be surjective; if T is ...
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113 views

Normalize a diagonal matrix such that each element belongs to $[0,1]$.

Let $\mathbf{x}\in\Bbb{R}^n$ be an $n$-dimensional real vector and $C\in\Bbb{R}^{n\times n}$ be a diagonal real matrix. Suppose that two vectors $\mathbf{r}_\min,\mathbf{r}_\max\in\Bbb{R}^n$ ...
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0answers
21 views

Deriving the formula for Fixed-rate mortgage using z-transform

So, using z-transform, one could easily derive the formula for fixed-rate mortgages. However, when I tries this, I noticed one thing I'm very uncertain of. The relationship for fixed-rate morgages ...
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2answers
17 views

how to map series of coordinates onto a series of coordinates with different resolution

I have a set of target coordinates and a set of actually clicked coordinates which should be approximately the same, but not identical. The y coordinates are equal, however, the x-coordinates differ, ...
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1answer
28 views

Find inverse $z$-transform of $\frac{5}{z^{2}-z-6}$

How can I find inverse z transform of $$X(z)=\frac{5}{z^{2}-z-6}$$ What I did: first i factored denominator and i got (z+2)(z-3), now we get A(-2^{n}) + b(3^{n}). To get A and B i used Partial ...
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1answer
47 views

Find inverse $z$-transform of $\dfrac{(z-1)^2}{z^3}$

How can I find inverse z transform of $$X(z)=\frac{(z-1)^{2}}{z^{3}}$$ What I did: I am thinking to do Partial Fraction Decomposition or long division. Is there another method ?
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1answer
35 views

Help tranformation of random variables?

Let $X$ have the p.d.f $f(x)= \frac{x^2}9$ , $0 < x < 3$, $0$ otherwise, find the pdf of $Y = X^3$ I have this exercise, but I do not know how to start, how do I know if it is a one to one ...
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2answers
27 views

Image of $A \subset \mathbb{R}^2$ under general transformation

If I have a transformation $\varphi: \mathbb{R}^2 \to \mathbb{R}^2$ which doesn't have any particular property, for example, which is not linear, how do I know what is the image of a subset $A \subset ...
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3answers
213 views

Calculate centers of circles from their ellipse perspective.

Originally there are 4 circles in a plane and after perspective transform we get four conics. Now I know the equation of those ellipses. How could I get the origin of those four circles ? I know it'...
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29 views

Show the solution for $\mathcal{F}(e^{-\left | t \right |})$ [closed]

I'm trying to show that $$\mathcal{F}(e^{-\left | t \right |}) = \frac{2}{\sqrt{2\pi}(1 + w^2)}$$ Knowing that the Fourier transform is in the form $$\mathcal{F}(f(x)) = \frac{1}{\sqrt{2\pi}}\int_{-\...
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14 views

Where do $H(3,1)$ and $H(3,2)$ come from when building Homography?

So you're given 4 pairs of points, including the original and where it maps to, i.e. $(x_1, y_1)\Rightarrow (x_1', y_1')$, $(x_2, y_2)\Rightarrow (x_2', y_2')$, $(x_3, y_3)\Rightarrow (x_3', y_3')$, $(...
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1answer
112 views

Determine shift between scaled rotated object and additional scale step

I am trying to find the amount to move an object so that, when it rotates and resizes, the resize would be smooth. I have a Qt program, where I have to rotate objects around center, and resize based ...
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55 views

Prove something is not a linear transformation

As I understand it, the two things that define a transformation as linear are: 1) $T(u+v) = T(u)+T(v)$ 2) $T(cu) = cT(u)$ I want to prove that $T(x,y) = x+y+1$ (where $T: \mathbb{R}^2\to \mathbb{R}^...