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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Probability Theory - Transformation (of two variables) of continuous random variables

Let $X_1$ and $X_2$ be independent and identically distributed continuous random variables, with probability density function $$p(x)=\begin{cases} \exp(-x), & \text{if}\ x>0 \\ ...
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1answer
60 views

Transformation of continuous, independent random variables

Let $X_1$ and $X_2$ be independent and identically distributed continuous random variables, with probability density function $$p(x)=\begin{cases} \exp(-x), & \text{if}\ x>0 \\ ...
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2answers
59 views

Probability Theory - Transformation of independent continuous random variables

Let $X_1$ and $X_2$ be independent and identically distributed continuous random variables, with probability density function $$p(x)=\begin{cases} \exp(-x), & \text{if}\ x>0 \\ ...
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0answers
46 views

How do I find the matrix with respect to a different basis?

I tried to solve this question but the answer is totally different, can you explain how to solve it
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32 views

Transformation Matrix for Derivative

I have figured out how to show Part A by using properties of derivatives. For Part B, we know that $T(f)$ is $\begin{pmatrix} 4a+2b+c\\4a+b\\2a\end{pmatrix}$, so when asked to find a matrix $A$, ...
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2answers
29 views

How do I scale a triangle given its cartesian cooordinates?

Given the cartesian $(x,y)$ coordinates of three points $a, b$ and $c$ that form an equilateral triangle $ABC$, how do I scale them using its center point so that its position on the cartesian plane ...
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1answer
45 views

If T is a normal transformation, does that mean that $||v||^2=||Tv||^2$?

If T is a normal transformation, does that mean that $||v||^2=||T||^2$ for all $v\in V$ ? Where $V$ is a vector space And if yes, how to prove it? EDIT: To be clear I mean that $||v||^2=(v,v)$
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29 views

Proving a property for a normal transforation $T$ for which $T^{-1}=-T$

Let $V$ be a unitary space. Given a normal transforation $T$ for which $T^{-1}=-T$. Let $v \in V$ and $u=Tv$ I need to prove that $Tu=-v$ (which I managed to do easily, so we can consider it as ...
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2answers
81 views

Closed form solution to rotation in arbitrary many planes in arbitrary dimensions.

In each coordinate space $V$ with dimension $\dim(V)$, we can describe any rotation operator $R : V \to V$ as a product of rotations in as few as $\dim(V) - 1$ orthogonal planes in the space. Let's ...
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0answers
30 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 $P$? ...
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1answer
33 views

Jacobian of the Transformation Problem, Multivariable Calculus

I have the following Jacobian problem: I'm having trouble working through it because the double integral in terms of u and v is throwing me off. Could someone walk me through it? Thanks!
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41 views

Linear Algebra, Linear Transformation problem [closed]

My task is this I am wondering how to go about doing this. Anyone have ant idea? Thanks!
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1answer
88 views

Rotate points from one plane to another

I'm trying to create a algorithm that will rotate points given on plane 1 to plane 2. I have found two different ways of doing this. My question is ... Why are the transformation matrices different ...
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26 views

Rotating points from one plane to another plane

I'm trying to create a function that will rotate points given on plane 1 to plane 2. I have found two different ways of doing this. The attached spreadsheet shows the two different ways as Solution ...
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0answers
11 views

aligning a matrix to reference matrix

Assuming X$_0$ as a matrix which represent some sort of transformation between TWO different coordinate system. Now, as a function of time the matrix which has three column vectors evolves in to X'. ...
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1answer
39 views

differential equation problem with laplace - calculators cant solve

I am trying to solve a third order differential equation problem with laplace transform. But I am stuck since 3 days... Could someone tell me what I did incorrectly? I transformed my equation in the ...
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1answer
28 views

How do I find the limits of a joint density function and calculate the inequalities?

The r.v.'s ${X_1}$ and ${X_2}$ are independent and equidistributed with density function $$ f_X(x)=4x^3, 0 \le x \le 1, $$ and equal to zero otherwise. Set ${Y_1=X_1\sqrt(X_2)}$ and ...
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0answers
10 views

Eliminating correlation by change of variables (on a sphere)

I am trying to understand the derivation of the mean of stationary points $\mathbb{E}[\mathcal N_s^+]$ of a Gaussian random field $V(x_1,\dots,x_N)$ on the upper half of a sphere with radius $R$ as ...
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1answer
43 views

What is the name of this matrix?

I have a vector $a=[a_1 \space a_2 \space a_3 \space a_4 \space a_5 \space \cdots a_n]$ and I want to generate following matrix 'A' from it. $$A=\begin{bmatrix}a_1 & a_2 &a_3\\a_2 & a_3 ...
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0answers
12 views

How to transform a set of scores into a normal distribution score?

I have a set of people with scores. Let's say: Person1: 18 Person2: 1,879 Person3: 873 Person4: 1M ... Person2M: 9,387 I would like to give each of these, a 0-100 Score, that is distribution in a ...
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0answers
59 views

Find transform matrix that transforms one line segment to another

I have two line segments, one with points $P_1=(x_1,y_1,1), P_2=(x_2,y_2,1)$ and other with points $P_3=(x_3,y_3,1), P_4=(x_4,y_4,1)$. I need to find transform matrix $$M=\left(\begin{array}{ccc} a ...
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1answer
17 views

about Fourier transform. graph of frequency over amplitude

I want to compute the Fourier transform for the function $f(x)=\sin{x}$. The first question is: the Fourier transform is $\pi$? $$a_n=\frac{1}{\pi}\int^{\pi}_{-\pi}{\sin{x}\cos{nx}}=0$$ ...
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15 views

2D Homogeneous Transformation : Reflection vs Mirroring

I have two questions: (1) Is there any difference between the terms Reflection and Mirroring in 2D Transformation? (2) What are their Transformation matrices with reference to an arbitrary line?
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24 views

Unitary similarity transformations

A complex matrix is said to be "normal" if it commutes with its conjugate transpose. Can you show that a matrix is normal if and only if it is diagonalized by a unitary similarity transformation? ...
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27 views

Similarity transformation-proof of equivalence

I am getting stuck with following problem: Show that \begin{align} \dot{x} = f(x/t) \end{align} is equivalent to \begin{align} \dot{y} = (f(y) − y)/t \end{align} using the transformation ...
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47 views

Convert Angular Velocity to an Euler Rate (Pitch/Yaw/Roll)

So for a physics simulation I'm developing I need to convert my angular velocity vector to a change in Roll/Pitch/Yaw. Until recently I've been doing this: parent.rotationYaw+=angularVelocity.Y; ...
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2answers
28 views

How to find the conjugate transformation when the matrix representing the transformation is unavailable?

I have a transformation $T:M_{nxn}^R \rightarrow M_{nxn}^R$ which is defined as follows: $T(A)=A^t$. Correct me if I'm wrong but I don't think it's possible finding the matrix representing the ...
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26 views

How to solve this fourier transform

Function is: $v(t)=4$ for $0< t< \frac\pi2$ $v(t)=-4$ for $-\frac{\pi}{2}< t< 0$ $v(t)=0$ for $-\pi< t< -\frac \pi2$ and $\frac\pi2< t< \pi$ I solved this and got : ...
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0answers
30 views

Inverse Laplace Transform by Partial Fraction Expansion

I've been trying to solve this partial fraction for a Laplace transformation but I can't. Is there any way to solve it? $$\frac{(s-t)^2}{((s-t)^2-1)((s+1)^2+4)}$$ Could somebody help, I've been ...
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1answer
17 views

Measuring Image of a Set Using Jacobian Integral

Assume $T:\mathbb{R}^d \to \mathbb{R}^d$ is a differentiable mapping and $E$ be a measurable set. Show that $m(T(E))=\int_E |det(DT(x))|dx$. I am thinking I might use the following Theorem, but ...
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2answers
35 views

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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0answers
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
43 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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1answer
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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1answer
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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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
89 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 ...
4
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1answer
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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1answer
22 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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2answers
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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1answer
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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1answer
39 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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0answers
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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52 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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0answers
17 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 ...