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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Image of $A \subset \mathbb{R}$ under transformation $(x,y) \rightarrow (u,v)$

What is the image of the set $$A=\{ (x,y) : 0\le x \le a\ , \ 1\le y\}$$ under the transformation $(x,y) \rightarrow (u,v)$ where $$u=x/y$$ $$v=x$$ The parameter $a$ is positive. I got a 'triangle' ...
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Showing that a transformation $T:\mathbb R^3 \to \mathbb R^2$ is linear

OK, I am trying to prove the following transformation is linear, and find the basis for $\ker(T)$ and Im$(T)$ (also denoted in our textbook by $N(T)$ and $R(T)$ ). Then we're suposed to find the ...
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141 views

Why do we define a linear transformation to have the property that $f(cW)=c f(W)$?

Why we define a lin tranfs to have the property that $f(cW)=c f(W)$ ? let $V,T$ be any two vector spaces and let $f:V\rightarrow T$ be a linear transformation between $V $and $T $ why do we ...
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198 views

Fourier transform for a 2D curve

I am stuck on the following problem about a Fourier transform of a 2D curve: I have to calculate the Fourier transform (using 1D complex FT) (and the opposite of it) for a 2D curve z(t). The curve is ...
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64 views

Function to map a range of $[-1,1]$ to a range of $[0,1]$ [duplicate]

I'm not capable of 'rigorously' defining the problem I have but this is the best I can do. If I have a set of points that range from $-1$ to $1$ inclusive and I have to transform the data so that it ...
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70 views

Stabilize Variance for Statistics (Transformation)

Problem: When $Y (> 0)$ has mean and variance equal to $\mu$ and $\mu/n$ respectively, it is shown in the textbook that the appropriate transformation of Y to stabilize variance is the square root ...
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99 views

Möbius transformation question

Möbius transformation copies the annulus $\{z:r<|z|<1\}$ to the domain between $\{z:|z-1/4|=1/4\}$ and $\{z:|z|=1\}$ Please help me to find what is $r$.
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423 views

Understanding perspective transform matrix elements interpretation

I am representing 3D points (vectors) in the following way: ...
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41 views

Inverting a discrete linear transformation

Consider the transformation from the set $\{a_n\}_{n=0}^N$ to the set $\{p_j\}_{j=0}^N$: $$ p_j = \sum_{n = 0}^Na_n\phi_n(x_j)$$ where $\{\phi_n(x)\}_{n=0}^N$ is a set of basis functions (linearly ...
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126 views

Finding an Orthogonal Transformation with 2 given vectors

There are two possible orthogonal transformations of $\mathbb{R}^2$ that leave the origin fixed and send the point $(0,13)$ to $(5,12)$. Find their matrices and describe them geographically. Can ...
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21 views

From parameterform to parameterfreeform

I have got the answer $\frac{1}{8}(30x-2y+21z+20)=0$ to an equation of a plane but I want the answer to be in parameter free form
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69 views

Find a vector from a given vector transformation matrix [closed]

if anyone can give an explanation on how to solve 10.f, that would be great, thanks! Find an: $$\vec x$$ such that: $$T(\vec x) = \begin{bmatrix}2\\1\\3\end{bmatrix}$$ The whole question is here ...
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185 views

Canonical form of a curve (geometry)

I am bothering with this geometric problem more than half a day and couldn't understand it yet. Here it is: In orthonormal coordinate system K=Oxy we have a curve C: $9x^2 - 4xy + 6y^2 + 6x - 8y + ...
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Laplace, Legendre, Fourier, Hankel, Mellin, Hilbert, Borel, Z…: unified treatment of transforms?

I understand "transform methods" as recipes, but beyond this they are a big mystery to me. There are two aspects of them I find bewildering. One is the sheer multiplicity of such transforms. Is ...
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1answer
82 views

What is the image of $D=\{z:0<\operatorname{Re}z<\pi\}\setminus\{\pi/2\}$ under $f(z)=\tan z$?

What would be the image of the domain $D = \{z:0<\operatorname{Re}z<\pi\} \setminus \{\pi/2\}$ under $f(z) = \tan z$? I havn't met with tan(z) transformation so I don't really know how to ...
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Is perspective transform affine? If it is, why it's impossible to perspective a square by an affine transform, given by matrix and shift vector?

I'm a bit confused. I want to program a perspective transformation and thought that it is an affine one, but seemingly it is not. As an example, I want to perspective a square into a quadrilateral (as ...
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88 views

Inverting an infinite sequence transformation

Consider a sequence $\{b_k\}$ define via: $$ b_k = \sum_{n=0}^\infty \frac{(n+k)!}{n!}a_n. $$ I would like to invert this transform. That is, I would like to know the coefficients $c_{nk}$ such that ...
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55 views

Can't figure out this transformation matrix

So basically I want to write a transformation matrix to take me out of one coordinate system and into another. The transformation has to be as follows: 1) The positive z axis normalized as ...
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97 views

Find $Y=f(X)$ such that $Y \sim \text{Uniform}(-1,1)$.

If $X_1,X_2\sim \text{Normal} (0,1)$, then find $Y=f(X)$ such that $Y \sim \text{Uniform}(-1,1)$. I solve problems where transformation is given and I need to find the distribution. But here I ...
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74 views

Calculating Fourier Transform of $1/|t|^n$

I have found the Fourier Transform of $x(t)=|t|^{n}$ and i can't calculate the Fourier Transform of $x(t)=|t|^{-n}$. Any suggestions?
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331 views

Simple Graph Transformation Question $\rightarrow$ $1/f(x)$

for the graph: such that the function is : $ y = \frac{a+x}{b+cx} $ where a = -2, b = 1 and c = 1/2 how do you sketch the graph of $ y = |\frac{b+cx}{a+x}| $ ?? i got that the VA of the new ...
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52 views

Need help understanding a transformation

I know this might be an unusual question, but please bear with me. In the book ¨An Introduction to Maximum Principles and Symmetry in Elliptic Problems¨ There is the following example of ...
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166 views

What are the units of Singular Value Decomposition components?

I have a symmetric variance/covariance matrix $A$ which is of size (27 x 27). I know that it's rank deficient (rank = 21). I also know that the units of $A$ are $m^2$. I am trying to use Singular ...
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122 views

Basis of kernel and image of a linear transformation - verification

The transformation matrix I found is: $$\begin{pmatrix} 1 & -1 \\ 1 & 1 \\ 0 & 0\end{pmatrix}$$ Is this how a basis for $\ker$ and $\mathrm{im}$ is calculated? $$\begin{pmatrix} 1 & ...
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156 views

Harmonic Function Transformation Help

Consider the harmonic function $$u(x,y)=1-y+\frac{x}{x^2+y^2}$$ on the upper half plane $y>0$. What is the corresponding harmonic function on the first quadrant $x>0$, $y>0$, under the ...
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35 views

Transformation of binary data

I have a function that I try to optimize using Particle Swarm Optimization. Objective function gets a binary string. So these binary strings are candidate solutions of the subject function. I can ...
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1answer
67 views

Special linear transformations

Special linear transformations are matrices with determinant equal to 1. What additional properties do such transformations have compared to "regular" linear transformations?
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66 views

Perhaps an easy algebra problem, but it still evades me

I need help spotting a corresponding transformation Let $x,y$ be some variables and $$z=z(x,y)$$. We have a transformation $X(\lambda):(x,y,z)\to (x',y',z')$, such that $$x'= x\exp(a\lambda)\\ ...
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40 views

Relationship between three matrices

I think this might be an odd question, and a little vague. But here goes. This is related to coordinate transformations. Three matrices are given: $G_1 , G_2$, and $\Lambda$. $G_1$ and $G_2$ are ...
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73 views

Groups of transformations

I tried to find literature and articles about groups of transformations, but mostly what I found is either about groups or about transformations. Can you suggest me literature where groups of ...
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Linear Transformation Orthogonality

True or False: If $T$ is a linear transformation from $R^n$ to $R^n$ such that $$T\left(\vec{e_1}\right), T\left(\vec{e_2}\right), \ldots, T\left(\vec{e_n}\right) $$ are ...
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1answer
160 views

Result of multiplying a scaling matrix with a rotation matrix

I don't understand why if you multiply a scaling matrix with rotation matrix that the resulting matrix, when applied to a shape like an ellipse, only gets scaled and does not get rotated. ...
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75 views

Following a polyline along the surface of a polygon that is twisted

I have (hopefully) an interesting problem regarding geometry. I will also search online and in literature but I thought to pose the question here as a third resource. For my problem I need to get the ...
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1answer
61 views

What's wrong with this Linear Algebra proof? Linear Transformation?

The question and proof is as follows: http://i41.tinypic.com/5ahvuc.jpg I get it up until the part where $u-\beta y \in W$. If this is true, then isn't $U=W$? Furthermore, how could a single vector, ...
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42 views

base transformation

Is there a smart way to make a base transformation matrix for one base to another? Here are my bases: $$ E_1= \begin{bmatrix}-0.4656 & -0.7461 & 0.4760\\ 0.8073 & -0.1377 & ...
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1answer
46 views

Need to find a Fourier Series…

I am to find a Fourier Series for the following function: $$ y(x)=\sqrt {R^{2}-x^{2}} $$ about $$ -R \leq x \leq R $$ with the recursion $$ y(x+2R)=y(x) $$ Do I let$\sqrt {R^{2}-x^{2}}$equal $y$ ...
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68 views

How do a transformation 'born'?

Well, there are several transformations in math. Like the laplace transformation. My question is about the utility and motivation of these transformations. Like, when we have an equation, and we ...
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1answer
126 views

Translation an orthogonal transformation?

Translation is when we move an object in an n dimensional space, to another point in the same space, It can be used to remove the mean of data points from a dataset, mathematically we can define by a ...
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How to solve cross-products including matrices?

I'm a programmer and I'm doing a whitebalance-transformation in RGB colorspace. This should work with this transformation matrix that I've found in literature: $$ \begin{pmatrix} R \\ G \\ B ...
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1answer
97 views

Trig, matrix transform, or…?

I am working on an app that will transform a figure such as this: Into this: In short, the grey "canvas" is deformed so that the inner black quadrangle is as close to a rectangle as possible, ...
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1answer
439 views

Discrete Time Fourier Transform example: $x = [1 \; 2 \; 3 \; 4]^T \; \rightarrow \; X=?$

How do I find the Discrete Fourier Transform of the sequence below? $$ x = \begin{bmatrix} 1 \\ 2 \\ 3 \\ 4 \end{bmatrix}$$ Show all steps.
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1answer
23 views

Which point on or inside or outside the frame move in a circular trajectory?

Which point on or inside or outside the frame move in a circular trajectory?
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99 views

Convert hermitian matrix to symmetric

Is there some simple transformation (or a simple way to find it) which would convert any given Hermitian matrix $A$ to a symmetric matrix $B$ with the same spectrum as that of $A$ (so I guess that ...
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1answer
398 views

Calculating a value inside one range to a value of another range

How does one calculate the value within range -1.0 - 1.0 to be a number within the range of e.g. 0 - 200, or 0 - 100 etc. ?
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71 views

Simplex preserving transformation in $\Bbb R^2$

I am looking for a transformation that preserves the vertices of a triangle located at the $\Bbb R^2$ simplex and moves a point at $(x_1,y_1)$ to a point inside the triangle $(u_1,v_1)$. I am hoping ...
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189 views

One circle, two lines Apollonius' problem

I've been trying to solve special case of Apollonius' problem, where instead of 3 circles i have 1 circle and 2 lines. Acording to: ...
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106 views

image of a circle under conformal trasformation

Consider a circle: $C_R=\{w=(x,y): |w|^2=x^2+y^2=R^2\}$ Prove that $A(C_R)$ remains a circle if $A$ is either a conformal or an anticonformal matrix. My attempt: I defined the complex number $z:=x ...
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39 views

Identity for reducing the power in the parameters of Hypergeometric functions

Is there any identity/formula for reducing/increasing the power in the parameters of the Gauss Hypergeometric function $ _2F_1(a,b;c;z^d)$ (d is a real) let's say to z? Is there also any identity for ...
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237 views

Hodograph transformation and implicit solution of a non-linear PDE

I am trying to understand how can one apply the Hodograph transformation to a non-linear PDE. I read that this transformation implies the representation of the solution in the implicit form . So, if I ...
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72 views

How to find a new point on rectangle based on an known point on the same?

I have rotated a rectangle a certain amount of degree and got the point(x,y)=(130,40) which was previously (152,60). Now i want to find the x,y(marked as red) value at another location based on the ...