The transformation tag has no wiki summary.
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0answers
28 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?
$$\begin{pmatrix} 1 & ...
0
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0answers
27 views
Harmonic Function Transformation Help
Consider the harmonic function $$u(x,y)=1-y+\frac{x}{x^2+y^2}$$ on the upper half plane $y>0$.
What is the corresponding harmonic function on the first quadrant $x>0$, $y>0$, under the ...
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0answers
23 views
Discretizing a cosine function?
I'd like to start by noting that for some fixed natural $N$ basis functions for my system will be generated by $f(k,x)$ as defined and explained here or in numerous other sources:
$$f(k,x) = \sqrt2 ...
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0answers
17 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 ...
1
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1answer
37 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?
2
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0answers
51 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
$$x'= x\exp(a\lambda)\\
...
0
votes
1answer
29 views
Relationship between three matrices
I think this might be an odd question, and a little vague. But here goes.
This is related to coordinate transformations. Three matrices are given: $G_1 , G_2$, and $\Lambda$. $G_1$ and $G_2$ are ...
1
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1answer
52 views
Groups of transformations
I tried to find literature and articles about groups of transformations, but mostly what I found is either about groups or about transformations.
Can you suggest me literature where groups of ...
1
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2answers
33 views
Linear Transformation Orthogonality
True or False:
If $T$ is a linear transformation from $R^n$ to $R^n$
such that
$$T\left(\vec{e_1}\right), T\left(\vec{e_2}\right), \ldots, T\left(\vec{e_n}\right) $$
are ...
0
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0answers
20 views
Transformation into cartesian coordinates
I need some help with specific transformations and rotations.
But first, I need to describe context.
Imagine two points in space situated at $(x_1,y_1,z_1)$ and $(x_2,y_2,z_2)$ respectively. In
a ...
0
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1answer
34 views
Result of multiplying a scaling matrix with a rotation matrix
I don't understand why if you multiply a scaling matrix with rotation matrix that the resulting matrix, when applied to a shape like an ellipse, only gets scaled and does not get rotated.
$$\left( ...
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0answers
27 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 ...
0
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1answer
41 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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0answers
13 views
Generalization/abstraction of an allocation problem
I'm having difficulty generalizing and finding the right abstraction for the following real world problem :
For each period, on a global segment, I know some data that is divided into intermediate ...
0
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1answer
27 views
base transformation
Is there a smart way to make a base transformation matrix for one base to another?
Here are my bases:
$$ E_1= \begin{bmatrix}-0.4656 & -0.7461 & 0.4760\\
0.8073 & -0.1377 & ...
2
votes
1answer
27 views
Need to find a Fourier Series…
I am to find a Fourier Series for the following function:
$$
y(x)=\sqrt {R^{2}-x^{2}}
$$
about
$$
-R \leq x \leq R
$$
with the recursion
$$
y(x+2R)=y(x)
$$
Do I let$\sqrt {R^{2}-x^{2}}$equal $y$ ...
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2answers
48 views
How do a transformation 'born'?
Well, there are several transformations in math. Like the laplace transformation. My question is about the utility and motivation of these transformations.
Like, when we have an equation, and we ...
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0answers
40 views
Dot Product in spherical coordinates
Given two vector $\vec{A}$ and $\vec{B}$. The dot product is given by
\begin{align}
\vec{A}\cdot\vec{B}=A^ie_iB^je_j=A^iB^j\left(e_i\cdot e_j\right)=A^iB^jg_{ij}
\end{align}
where $g_ij$ is the metric ...
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0answers
23 views
Translation an orthogonal transformation?
Translation is when we move an object in an n dimensional space, to
another point in the same space, It can be used to remove the mean of data points from a dataset, mathematically we can define by a ...
4
votes
1answer
40 views
How to solve cross-products including matrices?
I'm a programmer and I'm doing a whitebalance-transformation in RGB colorspace. This should work with this transformation matrix that I've found in literature:
$$
\begin{pmatrix}
R \\
G \\
B
...
1
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1answer
72 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, ...
1
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1answer
29 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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0answers
24 views
Invariance of inner product wrt coordinate transformation
Given two vector fields $A=\{A^1,A^2,A^3\}$ and $B=\{B^1,B^2,B^3\}$ I have to transfer them to spherical coordinates and compute the inner product and show that it is invariant. I already have ...
0
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1answer
14 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?
1
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0answers
13 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 ...
1
vote
1answer
28 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 ...
2
votes
1answer
48 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:
...
0
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0answers
27 views
Convert between View Matrix and Tuple of Camera Position, LookAt Vector, Up-Vector
given a View-Matrix $M$ that can transform world coordinates into camera space, how can I convert between this representation and a more human readable form of Position ($\vec p$), Look-at vector ...
0
votes
1answer
24 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 ...
1
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0answers
23 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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0answers
35 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 ...
0
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1answer
40 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 ...
2
votes
0answers
18 views
(Kleiner) transform preserves smoothness class
Consider the transform of nonnegative continuous concave positive homogenuous of first order function $f(x)$, $x \in \mathbb R^n_+$, $f \not\equiv 0$ given by
$$
f^\times(y)= \inf \left\{ \left. ...
2
votes
1answer
55 views
Finding a hyperbolic isometry that fixes the point $x = 2$ and $x = 17$
I know that a Mobius transformation is hyperbolic if the trace is $> 2$ which is $a + d$. But I'm not sure of the next steps involved to arrive at the answer.
2
votes
1answer
71 views
Find an orientation preserving isometry $f (z) = \frac{az+b}{cz+d}$ such that $f (i) = 17 + 3i$
This is probably a very simple questions but I am not clear on Mobius transformations and how to solve this problem. I'd appreciate if somebody can point me towards a method to do these sort of ...
1
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0answers
24 views
transforming a straight band into a logarithmic spiral
I want to plot the labels and the graduations of an historical timeline onto a logarithmic spiral.
If this timeline is on the $x$-axis, $-\infty$ would project to the center of the spiral, $+\infty$ ...
1
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2answers
79 views
Find the standard matrix of the transformation $T:\mathbb{R}^2\to \mathbb{R}^2$ that corresponds to the reflection through the line
Find the standard matrix of the transformation $T:\mathbb{R}^2\to \mathbb{R}^2$ that corresponds to the reflection through the line $x_2=2x_1$ followed by reflection through the line $x_1=3x_2$
I am ...
-4
votes
0answers
126 views
$[T]_{\scr{C}}=[T]_{\scr{B}}^{\scr{C}}[v]_{\scr{B}}$: A Desideratum for Creative Disquisition [closed]
$\blacklozenge\hspace{.2cm}$Consider the following data in this first litany:
$\hspace{2cm}\Diamond\hspace{.5cm}$$V$ and $W$ are finite-dimensional vector spaces.
...
0
votes
1answer
201 views
Value range of normalization methods? min-max, z-score, decimal scaling
I am working my way through Normalization (data transformation) of data and was curious about four methods:
min-max normalization, 2. z-score, 3. z-score mean absolute deviation, and 4. decimal ...
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0answers
30 views
Non-linear transformation preserving stereographic Riemannian metric on the sphere of radius R
I have been given a the Riemannian metric of a sphere of radius R in stereographic coordinates:
$$G=4R^4\frac{du^2+dv^2}{(R^2+u^2+v^2)^2}.$$ I have shown that this metric is preserved under rotation, ...
0
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0answers
17 views
Is $f_{\Theta|Z}(\theta|z)$ Gaussian when $Z = \theta^3 + V$, and given that $\Theta$ and $V$ are Gaussian?
$\Theta$ and $V$ are zero mean Gaussian random variables with variances $\sigma_\Theta^2$ and $\sigma_V^2$.
A third random variable $Z$ is defined as:
$$
Z = \Theta^3 + V
$$
Is ...
1
vote
3answers
90 views
transformation of integral from 0 to infinity to 0 to 1
How do I transform the integral $$\int_0^\infty e^{-x^2} dx$$ from 0 to $\infty$ to o to 1 and. I have to devise a monte carlo algorithm to solve this further, so any advise would be of great help
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0answers
23 views
Prove a transformation is a variational symmetry for J
The following problem is from The Calculus of Variations by B.von Brunt (page 215, Exercise 9.2.1)
Let
$$
J(y)=\int_a^b xy'^2\mathrm{d}x.
$$
Show that the transformation
$$
X=x+\epsilon2x\ ...
1
vote
1answer
62 views
extract [0 … 2PI] rotation from 3x3 homogeneous 2D transformation matrix
I'm trying to extract the angle [0 ... 2PI] from a 3x3 homogeneous 2D transformation matrix. In fact I've found 2 very helpful posts at stackoverflow and stackexchange.
...
1
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2answers
33 views
Please, I need a more detailed explanation of the particular solution of the problem with vectors
Here is the problem and its solution (link to the source if you are interested):
Two different points $A$ and $B$ are given. Find a set of such points $M$, that ...
3
votes
1answer
130 views
Finding the dimensions of subspaces of a Vector space and S-cyclic subspaces using minimal poynomials
I've been staring at a chapter in Bill Cooperstein's Advanced Linear ALgebra for some time now and one section is giving me trouble. It is about elementary divisors and invariant factors. My ...
-3
votes
1answer
47 views
Separating $x_1^{x_2}$ into sum of two terms by variable transformation
Given the function $f(x_1, x_2)$ in the form of product of two variables.
$$f(x_1, x_2) = x_1^{x_2}$$
I want to apply a variable transformation on this function, so that I can write it sum or ...
2
votes
1answer
43 views
Why is it called the “Unscented” transform?
I have not been able to track down the reason the Unscented Transform has the name it has. Can anyone shed some light on the meaning of the term "unscented" in this context?
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63 views
Way to Tietze's Transformation Theorem
during our knot-theory lecture we have talking about the following theorem:
Given two finite presentations of the same group, one can be obtained from the other by a finite sequence of Tietze ...
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0answers
47 views
Area of parallelogram using matrices.
A) Find the area of the parallelogram with verticies $(4,1),(7,-1),(5,2),(2,4)$.
Moving to origin $\rightarrow$ $(0,0),(3,-2),(1,1),(-2,3)$. Now, take the absolute value of the determinant of the ...
