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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Get vertex points of transformed rectangle knowing bounding box and transform matrices

(I'm not a mathematician so talk down to me). I have a rectangle that has been transformed by a series of matrix transforms. I can recover the transform matrices and get the x,y coordinates of each ...
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109 views

Transformations of RV's Ensuring Absolute Continuity of Quantile Functions

Given a real random variable $X$, suppose $T:\mathbb{R}\to\mathbb{R}$ is non-decreasing. Define $Y=T\left(X\right)$. Let $Q_{X}$, $Q_{Y}$ be the corresponding right-continuous quantile functions. ...
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1answer
23 views

Finding the area between two curves using a set of transforms and their Jacobian

I have the following transforms: $\begin{align} x &= u^2 - v^2 \\ y &= 2uv \end{align}$ and am tasked with finding the area between the following curves: $\begin{align} x &= 4 - ...
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3answers
2k views

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 number of them. Is there a unified ...
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1answer
27 views

What is known about the space of measure-preserving transformations?

I started reading about measure-preserving transformations, the ergodic theorems and mixing, but I was also wondering what is known about the space of measure-preserving transformations. The books ...
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4answers
47 views

Negation with De Morgan’s law

I'm having a hard time getting my head around transformation proofs. There is one particular example demonstration in the material I'm studying which I can't make sense of From this ¬ (¬ (¬ p) ∨ ¬ ...
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1answer
21 views

Transforming an integral to a different domain

For a given $v(x)$ with $x\in[0,1]$, use the variable transformation $x=g(\eta)=\frac{1}{2}\eta+\frac{1}{2}$ to transform the integral $I=\int_0^1v(x)dx$ to an integral over $[-1,1]$. My doubts: ...
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1answer
29 views

What is wavelet tranform in simple words?

I have read wiki and other sources and have still problem understanding the wavelet transform. What is the basic idea in simple words? Does the Fourier uncertainty hold for wavelet transform?
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2answers
63 views

Calculate Rotation Matrix to align k n dimensional vectors

I have a $k$ number of $n$-dimensional vectors written with respect to two rotated frames: $X= \{\vec{x}_1,\vec{x}_2,...,\vec{x}_k\}$ and the same rotated vectors: $X'= ...
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1answer
23 views

Image under $T_j$ of the basis vectors $e_1$ and $e_2$.

![image]: http://imgur.com/ll5Au7B Part B in the above link. I understand how to find the image under $T_j$ but I dont understand how to Plot the image set $T(U)$ of the unit square $U=\{te_1 + ue_2 ...
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5answers
2k views

Converting between two frames of reference given two points

I have two points ($P_1$ & $P_2$) with their coordinates given in two different frames of reference ($A$ & $B$). Given these, what I'd like to do is derive the transformation to be able to ...
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1answer
36 views

Finding a Transformation for a Sum of Exponentials

I am looking to see if it is possible to find a transformation $T_i(f(x))$ such that $$T_1\left(e^x+e^{ix}+e^{-x}+e^{-ix}\right)=e^x-ie^{ix}-e^{-x}+ie^{-ix}$$ ...
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0answers
3 views

Derivate formula for Radon-transformation

For the Radon-transformation $\mathcal{R}f(r,\omega)=\int_{\{x:x\cdot\omega=r\}}f(x)\mathrm{d}\sigma(x)$ with $r\in\mathbb{R},\omega\in\mathbb{S}^{n-1}$ I want to prove the following derivative ...
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2answers
48 views

Laplace transform of $\sin(\sqrt t)$

How can I use this differential equation $$4tf''(t) +2 f'(t) + a^2 f(t)=0$$ to show that $$L(\sin(\sqrt{t}))=\frac{1}{2}\sqrt{\pi}\,\frac{1}{s^{\frac{3}{2}}}\,e^{\frac{-1}{4s}}$$
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0answers
11 views

Abel transformation - sources

I'd like to study the Abel transformation, that is, $$Af(x) = \int\limits_x^\infty\frac{f(t)t}{\sqrt{t^2 - x^2}}\ \mathrm{dt},\quad x\in(0,\infty).$$ I'm especially interested in ...
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1answer
26 views

A Deeper Understanding / Interpretation of Homographies

I currently understand that a homography matrix, which allows for a mapping between planes in 3-dimensions, is a $3\times3$ matrix of the following general form: $$\begin{bmatrix} \vert & \vert ...
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2answers
86 views

Can anyone check these true and false statements about linear algebra?

For any square matrix $A$, the image of $A^7$ is contained in the image of $A$ I think this question is asking If $A^7x=b$, then $b$ must be in $A$ with some vector $y$ such that $Ay=b$. It Seems ...
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1answer
24 views

Area of Region using Transformation

Let R be the region bounded by the curves x = 0, y = sin(x)+1, y = sin(x), and y = 2 − x. Find the area of R. I need to use a transformation to find this, but I could not solve it using a ...
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1answer
50 views

Equivalent operations on Bezier curve points as control points?

In this question Explicit Bezier Curves: Lerping between curves same as lerping control points?, it shows that linearly interpolating between the result of evaluating two explicit bezier curves is the ...
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0answers
20 views

Zero Order Laguerre Transform of Sin(at)

Zero Order Laguerre Transform is given by $$L\{f(t)\}=\int_0^\infty e^{-t} L_n(t)f(t)dt $$ I've to prove ...
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0answers
58 views

Fourier Tansform of derivative on Wolfram Alpha

If I'm not mistaken, the Fourier Transform of the $n$th order partial derivative of a function with respect to $x$, using the transform variable $k$ is: $$(i*k)^n * [F(k)]$$ so for the $1$st order ...
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1answer
753 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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0answers
18 views

Transform matrix into constant diagonal matrix (or hollow matrix)

Does there exist a (possibly unique) orthogonal transformation, $U$, which will create a hollow matrix (or matrix with constant diagonal entries) from an arbitrary symmetric matrix, $A$? ...
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0answers
9 views

Conformal transformation of an annulus

I am given two circles in the complex plane, one of radius a, the other of radius b such that $a<b$. Their centres are separated by a distance h such that $a+h<b$. I need a conformal ...
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26 views

what is a ordinally quadratic function?

A function is ordinal equivalent to another means there exist a (unique) monotonic transformation between wiki definition of ordinal utility. I am a little confused, a function is ordinally quadratic ...
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37 views

inverse laplace tranform

I have a simple question, There are some functions $f(t)$, $g(t)$ and lets say $F(s)$ and $G(s)$ for the form of Laplace transform of $f(t)$ and $g(t)$, respectively. While I am solving ...
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1answer
457 views

Variance stabilization for Poisson data

Intro Let $Z > 0$ be a random variable with the mean and variance defined as $\mathbb{E}\{ Z \}$ and $\operatorname{Var}\{ Z \}$, respectively. The variance stabilization transform (VST) $f(z)$ ...
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0answers
17 views

What kind of transformation matrix should i use?

I am trying perform inverse kinematics on a 6 jointed robot, but is having a hard time determining how my transformation matrix should look like. I am using a piece of software to which you feed an ...
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1answer
21 views

Map an ellipsoid to a sphere

If I have a ellipsoid described by: $(\boldsymbol{x} - c)^T \boldsymbol{A} (\boldsymbol{x} - c) = 1$ How do I get the transformation to an unit sphere centered at the origin? From the principal ...
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0answers
35 views

How to obtain the given “analytical” solution to the 4th order ODE?

The 4th order ODE is $$(D^2-k^2)^2f=0, \qquad (1)$$ where $f=f(y)$, $D\equiv\frac{d}{dy}$, and $k$ is a constant. It is subject to the boundary conditions $f(0)=f'(0)=f(1)=0$. A solution to (1) is ...
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3answers
31 views

Why cannot the homogeneous coodinates be zero?

Given a point (x, y) on the Euclidean plane, for any non-zero real number Z, the triple (xZ, yZ, Z) is called a set of homogeneous coordinates for the point. Why can't Z be zero?
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1answer
44 views

How to skew a box to fit inside another under certain conditions

I guess my question is either fairly simple or impossible to solve. I have two boxes. One (I'll call child box) inside another (I'll call parent box). The parent box has width x and height y. The ...
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1answer
19 views

Find the matrix of ortogonal reflection

Let $e_1, e_2, e_3$ be an orthonormal basis for $R^3$ and consider the plane with equation $x_1 + 2x_2 - 2x_3 = 0$. Find the matrix of orthogonal reflection in that plane with respect to the given ...
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2answers
438 views

Interpret the graph of $\frac{ax+b}{cx+d}$ as a transformation of $y=\frac{1}{x}$

As part of a problem-set I'm self-studying, I'm trying to interpret the graph of $f(x)=\frac{ax+b}{cx+d}$ as a transformation of the graph of $y=\frac{1}{x}$, including determining what restrictions ...
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0answers
15 views

Partial Deviation of a Langrange-Function $L$?

$E$ is a transformation matrix which shall only do a rotation. Thus, $E^T * E = 1$. This requirement leads to an optimizing problem with a restriction which can be solved by Lagrange-optimization. To ...
2
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1answer
3k views

Negative & Positive Shear Factor

My question relates to constructional geometry & matrices aren't to be involved in the solution because stated Math level is up to O Levels... The figure below shows shear with y=3 as invariant ...
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0answers
18 views

Applying rotation matrix on inclined plane

I want to rotate an inclined plane to a flat surface. I think I can use the Euler angles to perform this operation. Using following points (Matlab): ...
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1answer
522 views
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1answer
9 views

How to calculate z transform of $x(n)=(n-1)(\frac{1}{2})^{n-2}u(n-2)$

Let $x(n)=(n-1)(\frac{1}{2})^{n-2}u(n-2)$, where $u(n-2)$ is shifted unit step function. How can I calculate z transform of this function? By definition, ...
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0answers
39 views

I'm looking for a rotation matrix for following transformation

I'm working with a 3D camera and I found out the formula to transform the camera measurements to real world coordinate system when you have a rotation around x and y (no z rotation). ...
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1answer
28 views

Using Fourier Transform to solve an ODE

Consider the differential equation $$f^{iv}+3f^{''}-f=g$$ I have read that taking the Fourier Transform of both sides gives ...
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2answers
71 views

Get the four corners of a rectangle

I have a boundary given ($xMin$, $yMin$, $xMax$, $yMax$) and the two points of a reference line of a rectangle. The begin point is at $(x_b, y_b)$ and the end point is at $(x_e, y_e)$. This ...
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0answers
36 views

Notation of the transformations in Linear Algebra

I am very confused with succinct notations of the transformations in Linear Algebra. When do we write each of the ways? What is the difference? In the lecture notes it says: T(x) = Ax = b in R^m, ...
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1answer
990 views

Finding reflection of a matrix

To 2 decimal places, what is the value of the lower-right entry in the reflection matrix $Q_a $if a = 1.05? Not even sure where to begin, is there a formula? This is what I could find in my textbook ...
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1answer
29 views

Homography with line correspondences

When calculating a homography with line instead of point correspondences, what is the derivation of the formula: $$ l_i = H^T\cdot l^{'}_i $$ I know that: $$ l^T\cdot x = 0 \quad\text{and}\quad ...
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0answers
12 views

Apply homogeneous transform to line parameters

I have a 2D range scanner mounted on a robot. This scanner is tilted around its x and y axes (meaning its scanning plane is not horizontal) with some unknown small angles. I initialize those roll and ...
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1answer
26 views

Concatenating two Rotation-Matrices

I have two $2\mathrm{D}$-planes in $3\mathrm{D}$-space with orientation parameters expressed as rotation $R_1$ and translation $T_1$ and rotation $R_2$ and translation $T_2$ with respect to some ...
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1answer
24 views

Mobius transforms which map the region ¨ (C \ D(1, 1)) ∩ D(0, 2) into the strip {|Im z| < 1}.

So far I have thought about first having my transformation, $T$, map $i$ to $\infty$ so that I get two parallel lines. But then I am not sure where to proceed from there.
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1answer
54 views

Why is this laplace identity true $\int_{\Bbb{R}^+}\frac{f(t)}{t}\,dt = \int_{\Bbb{R}^+}\mathcal{L}\{f\}$?

I was wondering why this laplace identity is true? Does it follow from definition? $$\int_{\Bbb{R}^+}\frac{f(t)}{t}\,dt = \int_{\Bbb{R}^+}\mathcal{L}\{f\}$$ I'm trying to understand the first ...