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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Invariance of stationary wavelet transform

Suppose we are given 64 points $x_1,\ldots ,x_{64}$ and divide them into two groups $x_1,\ldots, x_{32}$ and $x_{33},\ldots , x_{64}$. Then we apply stationary wavelet transform to both these groups ...
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3answers
38 views

Log transformation

Supose I have a series of numbers from 1 to 10. Their mean value is 5.5. Now supose I apply some transformation like $y=2x+1$. Now their mean value is 12. Now, if I want to get back the original mean, ...
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2answers
34 views

Rotation matrix construction

I'm reading a book on how to construct transformation matrices and I'm stuck in a certain point. From the book: Now here's the figure that I don't understand: How come the opposite edge in the ...
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1answer
23 views

Convolution Problem

while working on a signal processing problem i've reached to the following: So my aproach was: Am I doing something wrong? Is it valid Y(f)=[X(f) x H(f)]*W(f)=X(f) x [H(f)*W(f)] If you could ...
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1answer
20 views

Construction of a Transformation of a Random Vector that Preserves Independence

Let $X_1, \dots, X_n$ be $n$ independent random variables, not necessarily normal. Let $Y_1 = \sum_{i=1}^{n}\alpha_i X_i$ a given linear combination of the random variables. Is there a known, ...
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43 views

optimal monotonic transform: $\min_f (f(x)-y)^2$

Given two vectors of length $N$ denoted by $x_i$ and $y_i$, $1\leq i\leq N$, what is the monotonic transformation $f(x)$ that minimizes the overall distance $D=\sum_{i=1}^{N}{(f(x_i) - y_i)^2}$. Does ...
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1answer
20 views

How do I find the Probability Function of this Transform?

Given the Probability Generating Function for a non-negative, integer-valued, R.V. $X$ as: $$ g_X(t)=\log\left(\frac 1 {1-qt}\right). $$ How do I compute its Probability Function, $P(X=k)$? A ...
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12 views

Transformation Matrix for particular problem

I have a question regarding transformation matrices. I have two images both showing a table. I have coordinates of the corners of the tables, and now I want to apply a transform to 1 of the images so ...
2
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1answer
14 views

Finding Equality around Axis of Symmetry

I have a particular function that for even numbers $m$ obeys the following equation: $$f_{m,n}\left(\frac{2}{m}-x\right)=(-1)^nf_{m,n}(x)$$ Now when I put in odd values for $m$ and plot the ...
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1answer
45 views

Biliniear form to inner product

Let $f:V\times V\rightarrow F$ be a bilinear form in a finite inner product space V. If $F=R$, how can I prove that there exists a single linear transformation $T:V \rightarrow V$ so that for each ...
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1answer
139 views

Prove that every triangle is the orthogonal projection of an equilateral one

Prove that every triangle is the orthogonal projection of some equilateral triangle. This problem appears in a book I'm working through in the chapter on transformations in space. There is a rather ...
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1answer
39 views

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
48 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
51 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
42 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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2answers
28 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
26 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
40 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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1answer
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
80 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
28 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
27 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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1answer
38 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
37 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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15 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
26 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
9 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
42 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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11 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
33 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
15 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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11 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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21 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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2answers
22 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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0answers
23 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
20 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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0answers
25 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
25 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
13 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
21 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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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
33 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
17 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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0answers
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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2answers
41 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
80 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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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 ...