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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Transforming Vectors

Let $T$ be the linear transformation from $\mathbb{R}^3$ to $\mathbb R^3$ that reflects every vector about the $xy$-plane and then triples its length. How do I find the matrix for $T$?
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1answer
17 views

Given two linear transformations, find the preimage of a given point for the composite transformation

If someone could run quickly through the theory and methods on this it would be hugely appreciated. Thank you. Let $f: \Bbb R^2 → \Bbb R^2$ be reflection in the line $y = x$ and let $g: \Bbb ...
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10 views

How to get relative rotation matrix from two orientation values in android?

Following http://www.codeproject.com/Articles/729759/Android-Sensor-Fusion-Tutorial , I get two orientation values. Then, I transform those values to rotation matrices R1, R2. I think the relative ...
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22 views

Tricky change-of-basis transformation problem

I have absolutely no idea what to do here because of the $\sin(x).$ Let $V = \text{Span}\left\{x, x^3, \sin(x) \right\}$, and consider the basis for $V$ given by $\beta = \left\{x-2x^3, x^3+\sin(x), ...
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3answers
130 views

What is the kernel? give a basis of the kernal [on hold]

Let $P_3$ denote the real vector space of polynomial functions of degree up to 3, i.e., $P_3 = \{ a_3x^3 + a_2x^2 + a_1x + a_0 \mid a_i \in R\}$. Consider the linear transformation $D : P_3 \to P_3$ ...
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22 views

How to find the Fourier Transform of the form $\frac{cos(2\pi t)}{t^2}$?

I'm having trouble on figuring out how find the Fourier Transform of the following function, and I'm not allowed to use the straight up definition of the Fourier Transform but rather use it's ...
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1answer
36 views

Does the Fourier Transform exist for f(t) = 1/t?

My professor says that the following function has a Fourier Transform: $$f(t) = \frac{1}{\pi t}$$ He said that all I have to do is apply some of the Fourier Transform properties and not the direct ...
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1answer
44 views

Linear Transformation and Matrices

I have been studying linear algebra for a while now, and I still can't understand the basic concept of linear transformation and the easy ''translation'' of them the matrices. I understand that every ...
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14 views

Wavelet Transform of a shift invariant function

I want to calculate the wavelet transform of a shift invariant function. For example Gaussian - $\exp{-\|x-y\|^2_2} $. There is no restriction on the wavelet basis that can be used here. Can anyone ...
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1answer
13 views

Clarification of a transformation step (probably very simple).

A simple and quick question. Have been sitting over it for a while now but i can't get it right: Could someone just clarify how this transformation has been done? $$\frac{(v+1)^2 ...
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1answer
36 views

Null Space of Transformation

I am given that $V$ is n-dimensional vector space over $\mathbb{C}$ and $T \in L(V)$. And $T$ has least $m$ distinct nonzero eigenvalues. How do I show that $\text{null}(T^{n-m}) = ...
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31 views

the Fourier transform of a constant

How to calculate the Fourier transform of a constant without the aid of duality property? In other words, how do I calculate $$ \int_{-\infty}^{\infty}e^{-j\omega t}dt? $$
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8 views

Confusion about coordinate transforms

Lets say I have a camera aligned with the world coordinates system. I rotate it by 180 degrees around the z axis and then by 20 degrees around its new y axis. I have been reading about Euler angles ...
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1answer
20 views

What is the image of this mobius transformation

Consider the standard mapping $w=\frac{1}{z}$. What is the image of the "half" plane above the line whose imaginary part is $c$, for the three cases of $c\gt 0 , c=0 , c\lt 0$? For $c=0$ obviously ...
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Transformation for two different boundary functions in Stefan problem

Peace be upon on all of you, I have one-dimensional Stefan problem. Let say we have two boundary conditions of $u(t,s_{1}(t))=g_{1}(t)$ and $u(t,s_{2}(t))=g_{2}(t)$, where $u$ is temperature, $t$ is ...
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1answer
13 views

Inverse rotation euler angles

I have three angles representing a rotation (Pitch, roll and yaw). I need the inverse rotation (working on coordinate system transforms). What I do now is transforming these angle to a rotation matrix ...
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61 views

Dimension of image of a skew symmetric map is even

If $A$ is a skew-symmetric linear transformation on a finite-dimensional Euclidean space, then rank $\rho(A)$ of $A$ i.e., the dimension of image of $A$ is even. I am trying for a geometric proof of ...
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54 views

Fourier transform of Gaussian - sin/cos/Heaviside step function.

I would like to drive the Fourier transform of the following equations: $f_1(x)=e^{\frac{x^2}{2σ^2}}\cos(nx)$, $f_2(x)=e^{\frac{x^2}{2σ^2}}\sin(nx)$, where $n=2πf$ ...
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1answer
11 views

How to create own transformation change of variables

Evaluate the following integral using change of variables. Draw the original and new regions of integration. $$\int\int_{R} \frac{1}{x^2-y^2} dA$$ where R is bounded by the lines ...
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1answer
15 views

Composition of linear transformations that preserve angles

Given two invertible linear transformations T1,T2 in L(V) that preserve angles i.e. $\frac{(T(u), T(v))} {∥T(u)∥∥T(v)∥} = \frac{(u, v)} {∥u∥∥v∥} $. How can I show that T1T2 and T-1 also preserve ...
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3answers
27 views

Matrix with linear transformation with reflection

Find the matrix of the linear transformation A which is the reflection in the line $y = \sqrt{2}x$ with respect to the standard basis in $\mathbb{R^2}$. I Have no idea how to approach this problem... ...
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37 views

Help me generalize what this divisor transform does.

I have an algorithm which takes as input the series expansion of: $$\frac{-(1 + ax(-2 + x + ax))}{-1 + ax} \tag 1$$ or expressed differently: ...
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23 views

Dot product significance in vector transformation?

Suppose we multiply a 3 component vector by some 3x3 transformation matrix. Is it correct, then, to say the following about the transformed vector? Each component of the transformed vector is equal ...
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31 views

Conformal mapping of part of an annulus

I have a question about conformal mapping. I am wanting to map annuli to some other simple domain (probably rectangular). I have an image of my problem below In image A. we see a standard annulus ...
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1answer
32 views

Determine if the following function is one-to-one and/or onto

$T(x,y,z) = (xy,yz,xz)$ For one to one, I made $(x,y,z)=(u,v,w)$ and solved. $$xy=uv\to y=\frac{uv}{x}$$ $$\frac{uz}{x}=w$$ $$xz = uw \to x = u$$ $$uy = uv \to y = v$$ $$vz = vw \to z = w$$ So ...
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1answer
37 views

What is the correct change of variables to yield convexity in this nonlinear optimization problem?

$$ \text{min. } x/y \\ \text{s.t. } 2\leq x \leq 3 \\ x^2+y/z\leq \sqrt{y} \\ x/y=z^2 \\ x,y,z\geq 0 $$ To transform this problem into a nonlinear convex optimization problem, both the objective ...
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1answer
21 views

How can I find the density function of Z?

I am trying to find the density function for Z, this is what I am doing but I am not getting an appropiate function, I don´t know if there is something wrong with limits of the intregral. Or if this ...
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1answer
27 views

What is $f(T)$?

Let a linear transformation $T:\mathbb{R}^3\to \mathbb{R}^3$ defined as $T(v_1, v_2, v_3) = (v_1, v_3 - 2v_2, -v_3)$. Calculate $f(T)$ where $f(X) = -X^2 + 2 \in \mathbb{R}[X]$ I'm not so sure ...
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1answer
52 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 $\chi^2$ ...
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31 views

Complex analysis question, maximum principle application

Let $\Omega=\{z, \text{Re}z>0\}$ Suppose that $f$ is continuous in the closure of $\Omega$ and $f$ is holomoprhic on $\Omega$ and there are constants $A<\infty $ and $\alpha<1$ such that ...
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31 views

Equation of smooth spline curve

This is a homework question a)Assume an equilateral triangle ABC of a side AB = a = 10.The coordinate of A is (5, 3).The slope of the segment AB is 2.This triangle controls a curve.This smooth ...
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1answer
15 views

transformation of conic section

Given is the conic section $x^2 +xy + y^2 +2x +3y -3 = 0$. The following tasks: 1.) What is the coordinate matrix $A_1 = M_{\beta} (\sigma) $ of the bilinearform? 2.) do the transformation and ...
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Bounds on Interpolated Transformation Matrices Times Constant

Summary/TL;DR: Given: 4x4 transformation matrices (one of translation, scaling, rotation), each a function of $t$:$$ M_0(t), M_1(t), M_2(t), \cdots, M_{n-1}(t) $$ Given: ...
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23 views

Two definition of Fourier's transformation agrees? [duplicate]

Definition 1: If $f\in L^1(R^n)$, $\hat{f} (s)=\int _{R^n} e^{-isx}f(x)dx$ Definition 2: If $f\in L^2(R^n)$, let $f_i \in$ {Schwartz functions} such that $f_i$ converges to $f$ in $L^2$, then ...
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16 views

How can I apply inverse Abel Transform to a Data?

I have a data with X values and corresponding Y values. When I plot intensity map (2D histogram) of the data, I get a good image. I want to apply inverse Abel Transform to this image. How can I do it? ...
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2answers
111 views

How to write this term compactly?

How can I write this term in a compact form where $a$ only appears once on the RHS (in particular without cases)? $T(a) = \begin{cases} a^2 &,\text{ if $a \leq 0$}\\ 2a^2 &,\text{ ...
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8 views

Rotate a point on circle by an angle such that the point attains a new coordinate axis.

I have this circle with known radius and centre w.r.t to both new and old coordinate axes given by NBase and Base respectively. I need to find a point P and Theta such that when vector OP is rotated ...
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1answer
25 views

Probability function and random variables

Given a Bernoulli r.v., W, which is derived from r.v. T(Poisson) (a)if T=0 then W=1 and b) if T>0 then W=0). One has to show that the sample mean (the proportion of 0s in the sample), is an ...
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5 views

Electromagnetic Wave Propagation as Nonlinear Transform

This Wikipedia page says that the electromagnetic wave propagation in air can be done by Freshnel transform: $$U_{0}(x,y) = - \frac{j}{\lambda} \frac{e^{jkz}}{z} \int\limits_{-\infty}^{\infty} ...
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1answer
34 views

Probability function (p.f) of a random variable

If we have a Bernoulli random variable W that is derived from a Variable T (Poisson λ), by the following rules W = (if T=0 then W=1 and if T>0 then W=0), I am having trouble finding the pf for W. Any ...
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1answer
33 views

probability: transformation of a random variable $Y = X^4 + 1$

Find the PDF of $Y = X^4 + 1$ if $X\sim\exp(\lambda)$. When a transformation is not one-to-one, we have multiple solutions for $X$. Take for example $Y = X^2$. Then \begin{align*} x_1 &= ...
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35 views

We have the ode $y''−x^{−1}y'+x^{−2}y=0$, if $t=x^{−1}$, then how to get the new ode? [duplicate]

We have the ode $y''−x^{−1}y'+x^{−2}y=0$, if $t=x^{−1}$, then how to get the new ode? I just want to know the name of this method.
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27 views

Box Muller Transform - Proving that Z is Normal Distribution

I'm studying the Box Muller transform and I cannot see how Z0 and Z1 represent standard normal distributions. I've looked at the wikipedia page for the box-muller function but they don't seem to have ...
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1answer
22 views

how to obtain transformation matrix A in y = Ax + b notation?

I'm trying to obtain original transform matrix A and its translation vector b From y=Ax+b equation. I have original values of vectors before transform and translation (x) and vectors after transform ...
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1answer
24 views

Finding the image of a linear transformation given other images

Suppose there is a linear translation $T: \mathbb{R^3} \rightarrow \mathbb{R^3}$ such that $$T(\begin{bmatrix} 1 \\ 0 \\ 1 \end{bmatrix}) = \begin{bmatrix} 2 \\ 1 \\ 0 \end{bmatrix}, \ ...
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1answer
30 views

Matrix representation, linear transformation , general question on linear algebra

Let $X$ be a finite dimensional vector space over $K$ and define $T:X\rightarrow X$ to be a linear transformation on $X$. If $\alpha, \beta$ are two different basis for $X$ then we know that the ...
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11 views

Matrix representation of T, and its relationship to its transpose (linear algebra)

I have two questions on matrix representation of $T$. Let $X$ be a finite dimensional vector space over $K$ and define $T:X\rightarrow X$ to be a linear transformation on $X$. If $\alpha, \beta$ are ...
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Finding the standard matrix for a linear transformation involving an integral [closed]

For given scalars $a, b, c \in \mathbb{R}$, define a transformation $T: \mathbb{R^3} \rightarrow \mathbb{R}$ by $$ T \begin{bmatrix} a \\ b \\ c \end{bmatrix} = \int_0^{\pi}ae^t + bsin(t) + ccos(t) ...
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12 views

Integration matrix

I want to do integration(summation) of a signal(x) using matrix multiplication. I am looking for a transformation matrix, I corresponding to integration such that F = I * x , where x is the signal ...
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10 views

Rotation in configuration space.

Let $R_\psi$ be the rotation in configuration space around a vector $\bf{e}_\psi$ for an angle $\psi$. How is that the space rotation in configuration space have: ...