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), ...

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How to rotate points given in square grid?

I really hope you can see this picture. So My question is 1) If the figure is rotated 90 degrees counter clock wise about Point O, then: $$a. G to _________$$ $$b. _________ to P $$ How would i ...
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15 views

Get the positions of a periodic system of labeled points in reference to another coordinate system

First of all, I'd like to apologize because I'm not familiar with the conventions (names and formats) used in the math community. The problem is the following, I have information about a Face ...
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1answer
48 views

Transformation of variables for a non-monotonic function

Question: Let $U \sim \mathrm{Unif}(−α, α)$ follow the uniform distribution on the interval $(−α, α)$ for some parameter $α > 0$ and consider the transformed random variable $X = \sin(U)$. ...
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21 views

How wil the parameters of a bi-variate normal distribution change if I rotate the x-y panel?

For a bi-variate normal distribution: If rho = 0, then the plot in x-y panel would look like: I'm wonder, if I rotate the ...
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15 views

Particularly Problematic Spherical Polar Problem

The question is as follows: Using spherical polar coordinates, find the volume of the solid specified by R $\leq$ 3 and $0 \leq \theta \leq \frac{\pi}{3} $. I have two big questions about this ...
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18 views

Transform Matrix Using Equation that Relates Elements

Consider a 10 x 10 matrix, $M$, that contains elements $a_{ij}$ I want to swap some of the elements around. I have an equation that relates the new co-ordinates, $b_{ij} = a_{ik}$, where ...
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101 views

Matrix transformation question. How can I solve this?

This is a practice question for my upcoming exam. I am finding it difficult to understand the approach and solve questions like these, especially when it comes to structured questions (non-multiple ...
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1answer
93 views

Random vector $(X,Y)$ is uniformly distributed on the disk. Find the joint distribution of $R=\sqrt{X^2+Y^2}$ and $\theta =\arctan (Y/X)$

Random vector $(X,Y)$ is uniformly distributed on the disk $D_r$ defined by $$D_r=\{(x,y)\in \mathbb R^2\mid x^2+y^2\leq r\}.$$ Find the joint distribution of $R=\sqrt{X^2+Y^2}$ and ...
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84 views

Calculate the density function of $Y=\frac{1}{X}-X$ where $X\sim U[0,1]$

I know that : $$f_X(x)=\cases{1 & $x\in [0,1]$\\0 & $x\notin[0,1]$}$$ Then: $$P(Y\leq y)=P(\frac{1}{X}-X\leq y)=P(X\leq\frac{1}{2}(\sqrt{y^2+4}-y))$$ as $$\frac{1}{x}-x=y\rightarrow ...
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26 views

Elliptic Coordinates - Inverting the transformation

The standard way to transform elliptic coordinates $(\mu, \nu)$ $\ to$ Cartesian coordinates $(x,y)$: $x = a \cosh(\mu) \cos(\nu)$ $y = a \sinh(\mu) \sin(\nu)$ Is there any way to get the ...
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30 views

Find the coefficient of partial expansion $\frac{2x+3}{(1-x)(1+0.5x+0.5x^2)}$

I want to decompose the equation: $$\frac{2x+3}{(1-x)(1+0.5x+0.5x^2)}=\frac{A}{1-x}+\frac{B}{1+0.5x+0.5x^2}$$ I found $A$ by multiple both side with $1-x$ and plug $x=1$. However, it is so difficult ...
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26 views

Linear Transformations, Linear Algebra

Let T:P3→P3 be the linear transformation such that $T(−2x^2)= −2x^2 − 2x$, $T(0.5x + 2)= 3x^2 + 4x−2$, and $T(2x^2 − 1)= 2x + 1$. Find $T(1), T(x), T(x^2)$, and $T(ax^2 + bx + c)$, where a, b, and c ...
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40 views

Transforming a sawtooth into a sinus with one parameter

Can you help me in finding the analytical expression of a function $f_\alpha(\theta)$, with one parameter $\alpha=(0,1)$ by which one can continously transform a sawtooth curve into a sinus? With ...
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1answer
44 views

Where should I learn the theory of transformation?

I am trying to learn the dihedral group in group theory and I feel a bit confused about the composition of rotation and reflection, here are my questions: In what area of mathematics will I learn ...
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1answer
27 views

Cosine of a triangular random variate

Good morning, I want to calculate the probability density function of a random variate $Z=cos(Y)$, where $Y=Φ_1−Φ_2$ and $Φ_{1,2}∼U(0,2π)$, that is both variables are uniformly distributed in ...
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25 views

For $X$ exponential with mean $\frac{1}{\lambda}$, find pdf of $X^2, X^3,$ and $e^{-\lambda X}$

Supposed to express the answers in terms of $\lambda$. I tried X^2 and did $F_Y(x)=P[Y \leqslant X]=P[X^2 \leqslant x]=P[-\sqrt{x} \leqslant \sqrt{x}]$ Then this equals $F_X(\sqrt{x})-F_X(-\sqrt{x})$ ...
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53 views

How is double integral variable substitution different from one variable trigonometric substitution?

I'm studying variable change in double integrals and I understood the reasoning behind the formulas as described really well here. However, geometric arguments for analysis don't convince, as well as ...
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1answer
15 views

Determining the distribution of univariate transformation

If Y is uniformly distributed on the interval $(0, 1)$ and if $Z = –a * ln(1 – Y)$ for some $a > 0$, then to which of the following families of distributions does Z belong? Lognormal ...
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18 views

Probability of no heads in terms of a moment generating function

Define a R.V. $N \geq 0$, and let $M_N(s)$ be the associated transform. Assume that we have an unfair coin which lands heads with probability p and we toss it N times independently. Show that ...
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1answer
42 views

Can the equation $\cfrac{n^2(s-2)-n(s-4)}{2}=2^p-1$ be transformed into an equation of the form $x^2 + D=AB^y$, for fixed $s$, $s \ge 3$

Can the equation $\cfrac{n^2(s-2)-n(s-4)}{2}=2^p-1$ be transformed into an equation of the form $x^2 + D=AB^y$ (where $D,A,B$ are fixed and $x,y$ are variables) when the variable $s$ is fixed to any ...
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52 views

Linear Transformation: Orthogonal Projections

Define $\mathbf{u_1} =$ $\begin{align} \begin{bmatrix} 0 \\ 0 \\ 1 \\1\\ \end{bmatrix}\end{align}$ and $\mathbf{u_2} =$ $\begin{align} \begin{bmatrix} ...
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62 views

Steps of transformation

Given the function $y=-5-3 \sqrt{-2x-4}$ and base function y= $\sqrt{x}$ describe the transformations that have been applied to obtain the function from the base function. I tried, horizontal ...
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37 views

matrix transformation : shear, composition

Suppose T_m is the shear in the x direction with factor k, and suppose T_p is the rotation by angle \theta use matrix multiplication to find the image of the vector v=(1;2) under the composition T_p ...
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34 views

Does translating a function change its domain?

In Spivak's Calculus chapter 3, there is a part which essentially states: $\textrm{if} ~~~ r(x)=x^2\ \textrm{such that} \ -17\leq x\leq \frac{\pi}{3}\\ \textrm{then} ~~~ r(x+1)=x^2+2x+1=r(x)+2x+1\ ...
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39 views

A question concerning Jacobians of coordinate transformation

Apologies for perhaps a very trivial question, but I'm slightly doubting my understanding of Jacobians after explaining the concept of coordinate transformations to a colleague. Basically, as I ...
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1answer
17 views

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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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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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} ...
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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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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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26 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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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
54 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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78 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 $M>0$ ...
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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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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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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 ...
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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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175 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 ...
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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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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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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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31 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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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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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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51 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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26 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 ...