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2answers
137 views

Z-Transform Identity

I've come across an identity and would like to know if it has some sort of formal name or derivation or explanation or something! Also, I'm curious as to whether others are aware of such an identity. ...
3
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1answer
382 views

Möbius Transformation

Hey I am doing a basic undergraduate course in complex analysis and need some help on Möbius transformations. When determining the Möbius transformation does it really matter what 3 points I'm ...
3
votes
2answers
114 views

Put a transformation under the form of a rotation in the complex plane

On the complex plane, I have a transformation "T" such that : $z' = (m+i)z + m - 1 - i$ ($z'$ is the image and $z$ the preimage, $z$ and $z'$ are both complex number) and $m$ is a real number. ...
4
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1answer
103 views

Beta integral transformation

It's a homework task and I can't get past the last step. Task is to prove that $$ B(x,y)=\int\limits_0^1 \frac{\tau^{x-1}+\tau^{y-1}}{(1+\tau)^{x+y}} \mathrm{d}\tau $$ By substituting ...
3
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1answer
388 views

Coordinate transformation

I have some problems with a geometrical calculation. I want to know the coordinates of the point $P_2$ in my coordinate system $A \ (x,y,z)$ as shown in the following figure. Point $P_1$ (in $A \ ...
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1answer
533 views

Does null space always exist for a transformation?

This is inspired from this post as I was mentally playing with the concepts. The statement is the same just the transformation different, though for the benefit of everybody, I am repeating it, with a ...
5
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1answer
1k views

Finding the Dual Basis

Define the four vectors in $\mathbb{R}^4$ by $$v_1=\left( \begin{array}{ccc} 1 \\ 0 \\ 0 \\ 0 \end{array} \right), v_2=\left( \begin{array}{ccc} 1 \\ 1 \\ 0 \\ 0 \end{array} \right), v_3=\left( ...
1
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1answer
498 views

What is the Z-transform of a process shifted by a constant?

If $X(z)$ is the Z-transform of a discrete timeserie $x(t)$, what is the Z-transform of $x(t)+k$ where $k$ is a constant? From the linearity property of the Z-transform I would expect it to be $X(z) ...
1
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1answer
367 views

Given a matrix, find a linear transformation that uses it

The matrix is: $$\begin{pmatrix} 3+l & 8 & 3 & 3+l \\ 8 & 9 & 3 & 7 \\ 3 & 3 & 7 & 8 \\ 3+l & 7 & 8 & 13 \end{pmatrix}$$ I'm given the above ...
1
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0answers
191 views

2D Cartesian Matrix / coordinate transformation.

I has initially asked this question in the programming site but did not get an answer that worked. This is my first question on this site so please bear with me. Consider a page with three distinct ...
0
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1answer
176 views

Transformation Matrices [duplicate]

Possible Duplicate: Why can any affine transformaton be constructed from a sequence of rotations, translations, and scalings? Assuming that I have a set of points in a co-ordinate system (I ...
3
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1answer
3k views

Matrix for rotation around a vector

I'm trying to figure out the general form for the matrix (let's say in $\mathbb R^3$ for simplicity) of a rotation of $\theta$ around an arbitrary vector $v$ passing through the origin (look towards ...
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1answer
191 views

Prove equivalency of orthogonal transformation, $h(f(x),f(y))=h(x,y)$ and $f$ maps an orthonormal basis to another?

Please help! How do I go about proving this please? Let $f: M \longrightarrow M$ be a linear transformation. Then the following are equivalent: a) $f$ is an orthogonal transformation. b) ...
5
votes
1answer
947 views

How to figure of the Laplace transform for $\log x$?

I was looking at a table of common Laplace transforms of functions when I came across the transform for $\log x$. Apparently, the transform is as follows: $$\mathcal{L} \left\{ \log ...
2
votes
1answer
78 views

Change of coordinate codomain from $[-1,1]$ to $[0,1]$

Greetings to everyone! I've been searching around and thinking about how one translates coordinates from $[-1,1]$ to $[0,1]$ with little success. I am hoping someone here could help me with my little ...
0
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2answers
70 views

Normalize $X$ to $0$ to $10$ scale with asymptotes at either end

I am trying to find a scaling function that mimics the gas gauge in a car. I would like to map a value to a $0$ to $10$ scale, on which I have two known points. For example: $X_1 = 2$, $Y_1 = 2.5$, ...
1
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1answer
219 views

what is the “skewX” and “skewY” transform specified by flash's motion XML?

Flash has the ability to export animations into a format they call motion XML. Its specification is here I am trying to write a python renderer for these animations using pyglet. I understand ...
0
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1answer
330 views

Affine transformation matrixes

I could use some advise with the following problem: Lets say there is a cuboid that has two distinguished points - that is one of its vertexes ($A$) and the other one is somewhere on the surface ...
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0answers
538 views

2D Projective transform

Let's say we're transforming a square to an arbitrary 4 points via projective transform. Is there a way to ensure that the resulting points have homogeneous coordinates that are >0 ? i.e. sending ...
1
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1answer
611 views

rotating a rectangle via a rotation matrix

I want to rotate a 2D rectangle using a rotation matrix. After the rotation, I want the points (x, y) of the rectangle to be: ...
1
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0answers
319 views

How to project a spherical map onto a sphere / cube

I have this panorama, an spherical map from google streetview, and want to map this on a sphere/cube. Below are some examples and illustrations, i am going to implement it in c++ and are not sure ...
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2answers
4k views

How can I construct the matrix representing a linear transformation of a 2x2 matrix to its transpose with respect to a given set of bases?

I have been given that I am working with the space of all 2x2 matrices. The basis $B$ for this space is given as a set of four 2x2 matrices, each with an entry of 1 in a unique position and zeroes ...
0
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1answer
629 views

Finding the transformation matrix to transform one triangle into another

I have 2 sets of 3 points: the "origin" and "destiny". Any ideas on how to find the best-fit transformation matrix that will convert the origin's points to destiny using (only) rotation, scaling and ...
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2answers
1k views

Is a Fourier transform a change of basis, or is it a linear transformation?

I've frequently heard that a Fourier transform is "just a change of basis". However, I'm not sure whether that's correct, in terms of the terminology of "change of basis" versus "transformation" in ...
2
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1answer
102 views

How can I determinate the bases for the most simple representation of a linear transformation?

Imagine a linear transformation $\Phi : \mathbb{R}^4 \rightarrow \mathbb{R}^3$ with the ordered standard basis: $B = (\begin{pmatrix} 1 \\ 0 \\ 0 \\ 0 \end{pmatrix}, \begin{pmatrix} 0 \\ 1 \\ 0 \\ 0 ...
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1answer
99 views

General transformation matrix

I am currently working through some of my maths assignment, and i have this question, and i can't work out what it means, and i am sure there is something to missing which would make this question ...
0
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1answer
201 views

Need a transformation matrix to convert to new base vectors

I was searching for a solution, but can't find anything I can use with my superficial knowledge. So, I have vector A, vector B & vector C. I want to convert the space to base vectors A & B ...
0
votes
1answer
389 views

Plane transformation

I have a plane-A which sits on the origin and where every point on the plane has a z coordinate of 0 (so there is no rotation of the plane). I have plane-B in space and I have a a point (which is the ...
1
vote
1answer
576 views

Find 3D rotation vector and angle to transform a rectangle into a given quadrilateral

I have a given rectangle that I need to transform into a given quadrilateral shape that resulted from a rotation and translation in 3D space, and subsequent projection. ...
9
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3answers
4k views

Get Transformation Matrix from Points

I have built a little C# application that allows visualization of perpective transformations with a matrix, in 2D XYW space. Now I would like to be able to calculate the matrix from the four corners ...
2
votes
1answer
2k views

How to find the orthonormal transformation that will rotate a vector to the x axis?

I am having trouble remembering linear algebra. I need to find the orthonormal transformation that will rotate a 3-dimensional vector to the x axis. I could not find any similar question on the net. ...
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2answers
2k views

How can I determine the scale factor of a pantograph from the ratio of the arms?

I know this is probably simple but I just can't see it. How can I determine the scale factor of a pantograph from the ratio of the arms?
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1answer
343 views

What is the relation between complex numbers and transformation matrices?

I read addition and multiplication with complex numbers can be represented as translation and rotation in a 2D plane. I am using this to move around objects on the screen. I have an offset number, ...
1
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1answer
276 views

Is a linear conformal mapping same as a similarity transformation?

For a mapping between two Euclidean spaces, is it a linear conformal mapping if and only if it is a similarity transformation? My answer is yes, because the Jacobian matrix of a conformal ...
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0answers
294 views

Fast Walsh–Hadamard transform generalization for non-power-of-two orders?

I have to process vectors through a Hadamard matrix of order N. If N is a power of 2, I can use the Fast Walsh–Hadamard transform; but if N is not a power of two (for instance, N=12), it is not ...
0
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1answer
207 views

Finding the transformation matrix when transformations are given…

Question: For set of vectors {$x_1,x_2$}, $x_1=(1,3)^T, x_2=(4,6)^T$ are in $R^2$. Find the matrix of linear transformation $T:R^2\rightarrow R^3$ such that $Tx_1=(-2,2,-7)^T$ and $Tx_2=(-2,-4,-10)^T$ ...
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3answers
1k views

Is it true that any matrix can be decomposed into product of rotation,reflection,shear,scaling and projection matrices?

It seems to me that any linear transformation in $R^{n\times m}$ is just a series of applications of rotation(actually i think any rotation can be achieved by applying two reflections, but not sure), ...
1
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1answer
600 views

How do I map the torus to a plane?

Please see my answer on Perlin noise first. A bit of background. Imagine a solid texture, like an actual block of sky and cloud. If you "cut a sheet" of sky and display it as an image, you'd get ...
2
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1answer
1k views

Extracting perspective transformation from a 2D projection

I have a 2D projection of a flat, rectangular object in 3D space, like this one: I know all sorts of information about this shape—its opposite sides have the same length, the sides meet at right ...
0
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2answers
1k views

Any linear fractional transformation transforming the real axis to itself can be written in terms of reals?

I'm trying to teach myself complex analysis, and was reading about linear transformations. I would like to understand why any linear fractional transformation which transforms the real axis into ...
1
vote
2answers
112 views

Converting polynomials to depressed form

Given a polynomial of any degree $\sum_{i=0}^n a_ix^i$ can it be proven that the substitution $x=t-$${a_{n-1}}\over{na_n}$ will convert the equation to depressed form $b_nt^n$ + $\sum_{i=0}^{n-2} ...
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0answers
324 views

Joint distribution of transformed variables

I have a problem in deriving the transformed joint distribution for continuous random variables. The textbook says use jacobian which makes sense but I wanted to go from first principles like below... ...
0
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2answers
129 views

Transform/approximate this expression to avoid undefined value

I have an expression like this $$\sum_i^n\log\frac{x_i}{y_i}+\alpha\sum_i^nx_i\log\frac{x_i}{\beta}$$ A potential problem is that $x_i$ and $y_i$ may take value $0$ for certain $i$, hence making ...
1
vote
1answer
655 views

Isolate yaw-pitch-roll from rotation

I have a transformation that acts as such: $$RX=Y$$ Where $R_{3\times3}$ is a yaw-pitch-roll rotation matrix, and $X, Y$ are 3D vectors. Yaw ($\alpha$)-pitch ($\beta$)-roll ($\gamma$) rotations are ...
2
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2answers
238 views

Does this Laplace transform exist?

I had a final in differential equations with the first question being: "1. Does the Laplace transform of $\displaystyle \frac{1}{(1+t)}$ exist? Why or why not?" and number 2 was "2. If number one ...
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0answers
129 views

Hyperbolic Universal Covering Space

I have been working with Ricci flow in the euclidean and hyperbolic space but have been having considerable trouble determining how to generate a universal covering space for complex hyperbolic ...
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0answers
103 views

How do I transform the coefficients of a solved polynomial curve fit?

This all pertains to a piece of software I am writing but figured I'd get a better answer here than in Stackoverflow. I have no problem migrating the question if needed. Disclaimer: I am a software ...
2
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2answers
4k views

How to multiply vector 3 with 4by4 matrix, more precisely position * transformation matrix

All geometry in computer graphics are transformed by position * transform matrix; The issue is the fact that position is a vector with 3 components (x,y,z); And transform matrix is a 4 by 4 with one ...
0
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1answer
82 views

A few questions about linear transformations

$\phi \in \alpha(R^3,R^3)$ $B_c:\left(\begin{array}{rrr} 1&2&3 \\ 0&3&4 \\ -1&2&1 \end{array}\right) = [F]_C$ Determine the analytic form of the ...
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2answers
172 views

Modifying a discrete probability distribution according to set of weights

Given a discrete probability distribution (e.g., ${P_1=0.85,P_2=0.05,P_3=0.05,P_4=0.05}$), I would like to transform it according to some set of "weights" (say, ${w_1=2,w_2=0.5,w_3=1,w_4=0.5}$), which ...