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1answer
38 views

Compute the transformation in the given Basis

I forgot how to compute the transformation in a given basis. :'( For example, say I have the transformation \begin{equation}(a, b) \mapsto \begin{bmatrix}10a - 6b \\ 17b - 10b ...
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0answers
42 views

Z - transform of a transfer function

I have to apply a z-transformation to my transfer function which looks like this: $$\frac{K}{s} - \frac{K\cdot T}{T\cdot s}+1$$ I have tried it and this is my result: $$K \cdot \frac{z}{z-1} - K ...
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0answers
20 views

3D cartesian cordinates to 3D isometric cordinates

I am working on Isomer opensource project https://github.com/jdan/isomer and I need to convert 3D cartesian cordinates to 3D isometric cordinates. We already have 3D iso to 2D cartesian ...
0
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1answer
11 views

Transformation between 2D coordinate systems

Let there be two coordinate systems: unit coordinates at $(0,0)$, rotated by 45 degrees the same, but at $(5,5)$ How would I go about to create a transformation to convert #2 coordinates into #1 ...
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0answers
20 views

Variations of transformation of inversion?

Is there a transformation analogous to inversion, that is based on something other than circle (or sphere in higher dimensions), and has some interesting properties or applications? The motivation ...
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2answers
69 views

Question on transformations in the complex plane

In the image (part (b)), Since $z < |3|$ before the transformation, does that simply imply that the region to be shaded after the transformation is definitely the inside of the circle and not it's ...
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0answers
33 views

Using the Modulation property of the Fourier Transform

I'm working on a problem: Let $X(w)$ be the Fourier transform of $x(t)$. Find the transform of $y(t)=x(5t+3)\sin(2t)$ in terms of X(w). I am table to take the Fourier transform of $x(5t+3)$ and ...
0
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1answer
31 views

How can I convert an n-dimensional vector to a 2d point?

I have a n-dimensional vector / sequence of values, how can I convert it to a 2D representation of such vector? Follow-up: if I had a time-sequence in which every frame is n-dimensional, how can I ...
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1answer
29 views

The linear map $ T: \mathbb R^3{\rightarrow} \mathbb R^3$ with given matrix is a rotation about some line. Find the line.

Finals studying continued. $ T: \mathbb R^3{\rightarrow} \mathbb R^3$ with matrix $$A= \begin{pmatrix} -2/7 & 6/7 & 3/7 \\ 3/7 & -2/7 & 6/7 \\ 6/7 & 3/7 & -2/7 \\ ...
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0answers
18 views

Differential probabilities of transformed random variables

Let $X$ be a random variable with probability density function (pdf) $f(x)$ and let $Y = h(X)$ be a transformation on rv $X$. While calculating the pdf of $Y$, it is assumed that $Prob(x \le X \le x + ...
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0answers
22 views

Complex Variables Conformal Mapping in Complex Plane of harmonic Functions

Consider the harmonic function $u(x,y) = 1 - y + x/(x^2+y^2)$ 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
44 views

From inverse Weierstrass function to Jacobi elliptic/inverse elliptic functions?

As a conclusion to a previous question on integrals, I get an answer in terms of inverse Weierstrass elliptic function : $$ f\left(x\right)=\wp^{-1}\left( \beta + \frac{9\beta^2-1}{3(x-\beta)} \right) ...
0
votes
1answer
24 views

Finding an image (Linear Transformations) $T(2,-1,1)$

Let $T:R^3 \rightarrow R^3$ be a linear transformation such that $T(1,1,1) = (2,0,-1), T(0,-1,2) = (-3,2,-1)$ and $T(1,0,1)=(1,1,0)$. Find the indicated image $T(2,-1,1)$ I used the rule that: ...
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0answers
50 views

Help determining whether a function is a linear transformation $T:M_{2,2}\rightarrow R, T(A)=|A|$

Again, here is the function: $T:M_{2,2}\rightarrow R, T(A)=|A|$ I was able to prove that its not a linear transformation because $T(A+B) \neq T(A)+T(B)$ in fact, $T(A+B) = C$ where $C$ is a new ...
0
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1answer
13 views

Find linear transformation of a given matrix of linear transformation

I have two basis. The first is a $R2$ basis ${(1,0) , (0,2)}$. Lets call it basis of $U$. The second is a $R3$ basis ${(1,0,-1), (0,1,2), (1,2,0)}$ Lets call it basis of $V$. Is given a matrix of a ...
2
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1answer
39 views

Meaning of entries of a transformation matrix in practical terms [Homework related]

I'm having a bit of trouble understanding what the matrix entries mean practically in this problem: 100 kg of a highly toxic substance is spilled into three lakes. The state, t weeks after the ...
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0answers
31 views

Making a change of variable to transform an equation

$\displaystyle m\frac {dv} {dt} = mg - kv^2$ $\displaystyle\frac {dV}{dT} = 1 - V^2$ Make a change of variable $v=aV$ and $t=bT$, show that for suitable choices of the parameters $a>0$ and ...
0
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1answer
29 views

Defining a Linear Transformation Given a Basis for the Domain

I'm having difficulty understanding the proof for the following theorem: Suppose $B$ = $\{$$v_1$$, ... , $$v_n$$\}$ is a basis for a vector space V. Then for any elements $w_1$$, ... , $$w_n$ of a ...
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1answer
16 views

Matrix representations of linear transformation between bases

Let V and W be vector spaces, and let L: V -> W be a linear transformation between them. A basis for V is E = {$v_1$,...,$v_5$}. A basis for W is F = {$w_1$,...,$w_4$}. On the basis vectors the linear ...
0
votes
1answer
64 views

abs(x)cos(x) in Fourier space

I am working on some problems concerning Fourier Transform and I am facing something I don't understand. I am trying to understand what is the representation of the function f(x)=abs(x)cos(x) in the ...
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0answers
17 views

Basic Matrix Transformation

The information I have is for a matrix transformation from R^3 to R^3 (denoted by L()), L(a_1) = 3(a_1) and L(2(a_1))= (5,-3,6). Find L(3a_1-22a_1), L(-4a_1), L(0), L(4a_1). What I tried to do was ...
0
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1answer
64 views

Looking for a formula to calculate DCT/FFT frequencies when cropping a matrix/image.

Given: A is a matrix of dimensions W1 x H1 . Cropping: Few rows and/or few columns were deleted from matrix A. We got matrix B of dimensions W2 x H2. Not more than 5% of matrix A rows/columns ...
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2answers
45 views

How to prove this property of a projective transformation?

The copy below is from this book: Sophus Lie, Vorlesungen über Differentialgleichungen mit bekannten Infinitesimalen Transformationen, bearbeitet und herausgegeben von Dr. Georg Wilhelm ...
3
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1answer
67 views

How do digital filters work in time domain?

I am trying to understand how do digital filters work and how to actually calculate the output numerically. I have read that they are characterised by a transfer function $H(z)$ which results in a ...
0
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2answers
33 views

How does the transformation on a point affect the normal at that point?

Say I have a point in 3D with coordinates $\begin{bmatrix} p_1 \\ p_2 \\p_3 \end{bmatrix}$ and the normal on the point with coordinates $\begin{bmatrix} n_1 \\ n_2 \\n_3 \end{bmatrix}$. Now I apply ...
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0answers
32 views

How to calculate the combined frequencies of a DCT matrix?

Given a 2D matrix of dimensions w1,h1. I preform a DCT 2D transform on the matrix (DCT = DCT type 2). I get a 2D result matrix. This matrix has two frequency axes - x,y (which are simply the ...
0
votes
1answer
17 views

Non constant function of two points invariant under Affine transformation proof

Here is the question; Prove that there does not exist any nonconstant function of pairs of distinct points $P,Q\in\mathbb{R}^2$ or of triples of distinct non collinear points $P,Q,R\in\mathbb{R}^2$ ...
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0answers
13 views

Transformations on a $4\times4$ matrix

Let's say a company produces chips containing $16$ elements, ordered in a $4\times 4$-matrix: $$\begin{bmatrix} \hline ...
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0answers
29 views

Determine if the following linear transformation is surjective or injective

Let $S \left(\begin{bmatrix} x_1 \\ x_2 \\ x_3 \\ x_4 \end{bmatrix}\right) = $ $\begin{pmatrix} x_1 & -2x_2 & x_3 & x_4\\ 2x_1 & - 4x_2 & -3x_3 & ...
2
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1answer
45 views

Matrix representations of Transformation with change of basis (Fraleigh Beauregard)

I'm having problems understanding section 7.2 of FB's Linear Algebra, 3rd edition, and I can't find the solution online since no specific name is given to the matrices. Sorry for the long ...
1
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1answer
43 views

Impact of the transformation matrix distribution on linear transformation

Let $X$ be a $m\times n$ ($m$: number of records, and $n$: number of attributes) normalized dataset (between $0$ and $1$). Denote $Y=XR$, where $R$ is an $n\times p$ matrix, and $p<n$. I understand ...
0
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1answer
11 views

Find the basis of a transformation matrix for an endomorphism

I have a 3x3 transformation matrix $D_{BB} (f)$ with $B$ as a basis of vector space $V$ and $f$ as a diagonalizeable endomorphism $f : V \to V$ given. Basis $B$ is not explicitly given. The entries of ...
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0answers
26 views

is it all right my pf?

PB: Give a proof that the image of a circle under a linear transformation is a circle. (Let $z$ be a $z=z_{0}+Re^{it}$, $t$ is a angle.) I tried it. Can you check my pf? (is it all right?) My Pf) ...
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0answers
31 views

Using basic transformations to derive matrix for the reflection in a line?

Using basic transformations (translation, scaling and rotations), show all the steps to derive the transformation matrix for the reflection of points n the line : y = 3 - x I know that a directional ...
0
votes
1answer
60 views

Fourier Transform of rational function

So I have this function: $$f(t)=\frac{1}{(1-it)^{n+1}}$$ And I have the Fourier Transform defined as $$\hat{f}(\lambda)=\frac{1}{\sqrt{2\pi}}\int_\mathbb{R}f(t)e^{-\lambda.it}dt $$ Now my ...
2
votes
1answer
66 views

How does a cropping of a 2D matrix/image affect its DCT transform?

I apologize in advance: since I am not a mathematician, maybe my question is not well defined, but I hope that some of you will still understand my meaning. Given a 2D matrix, or an image of ...
0
votes
1answer
17 views

Rotation operator for a point in a coordinate system linearly derived from Cartesian coordinates

For some experimental and practical reason, I have created a new coordinate system in the form $$x^\prime_i=T_{ij}x_j$$ where $T_{ij}$ isn't a square matrix. $x_i$ is standard Cartesian coordinates, ...
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0answers
14 views

About representations and transformations under an $SU(n)$ Lie Group

I think my problem is that I misunderstand what "transforms under" really means. Let's take $SU(3)$, for the $\mathbf{3}$ with Dynkin indices $(1,0)$, a state transforms like : $ψ→gψ$. For the ...
1
vote
1answer
111 views

Joint density of two functions of random variable

This is online homework, and I'm not always clear on which chapter questions are from, so I might be completely off base. I have two random variables, $X_1$~UNI(5,10) and $X_2$~UNI(4,10), and then ...
0
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3answers
54 views

Let $T : \mathbb{R}^3 \to \mathbb{R}^3$ be a linear trasformation. Find $T(x)$

Let $T : \mathbb{R}^3 \to \mathbb{R}^3$ be a linear trasformation with $T \left(\begin{bmatrix} 1 \\ -2 \\ -1 \\ \end{bmatrix}\right) = \begin{bmatrix} 1 \\ -1 \\ 2 \\ ...
1
vote
1answer
31 views

Linear Transformations, kernels, and Basis for Range

I have the following question and am completely lost on how to start: Let $T: P_{2} \to P_{3}$ be the linear transformation $[T(p)](x) = p^{\prime}(x) + xp(x)$ Find $\ker(T)$ and find a basis for ...
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0answers
20 views

Rigid Deformation

I'm trying to parse through this paper on using the method of moving least squares for rigid transformations - http://www.cs.rice.edu/~jwarren/research/mls.pdf Under section 2.3, the author mentions ...
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0answers
13 views

Transformation Matrix of a function

I have the following: (Note: $V^{*}$ is defined as: $V^{*} = \{ L: V \rightarrow \mathbb{R} | \text{L is linear} \}$) Let $V$ be an $\mathbb{R}$-Vectorspace. Let $\phi \in V^{*} \text{ \ } \{0 \}$ ...
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0answers
12 views

scale transformation is invariant for H_1

Consider the subspace $H_1$ of $C_0(0,\infty)$, where $\phi=\int_0^t\dot{\phi}(s)ds$ and $\int_0^{\infty}{\dot{\phi}}^2ds<\infty$. The transformation is $(T\phi)(t)=t\phi(\frac{1}{t})$. How to ...
0
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2answers
21 views

Which, if any, of the following polynomials are in Range(t)?

Let T: P^2 ----> P^2 be a linear transformation defined by T(p(x)) = xp'(x) (i) 2 (ii) x^2 (iii)1-x I was hoping someone would show me how to find the range of one of them so I know how to do the ...
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2answers
38 views

Show that T is a linear transformation.

Let B be an element of $R^{n \times n}$ and define $T(A) = BAB$ for all $A \in R^{n \times n}$. Show that T is a linear transformation. I am completely lost and I do not know how to start this.
2
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1answer
87 views

Find linear transformation given kernel

$ F: R^4 -> R^3 $ $ kerF=span\{\begin{bmatrix}1\\2\\3\\4\end{bmatrix}, \begin{bmatrix}0\\1\\1\\1\end{bmatrix} \} $ Find linear transformation in canonical bases given above information. I tried ...
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vote
1answer
32 views

Function inverse mapping [0, +inf) to [0, 1)

I have a measure ($x$) which the domain is $[0, +\infty)$ and measure some sort of variability. I want to create a new measure ($y$) that represents regularity and is inverse related to $x$. It is ...
0
votes
1answer
67 views

How to find the rotation matrix that will align an arbitrary vector to an axis

If I have a vector that starts at the origin, how can I find the transformation matrix that will align it with the positive y-axis. So it basically turns into a positive-y axis? EDIT: I also forgot ...
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2answers
39 views

Linear operator exists then differentiable?

Let $E_{\text{open}} \subseteq \mathbb{R}^n$, and let $\vec{x_o} \in E$. Let $\vec{f}: E \rightarrow \mathbb{R}^m$. If there exists a linear operator $A: \mathbb{R}^n \rightarrow \mathbb{R}^m$. such ...