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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2
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1answer
180 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
vote
1answer
98 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
votes
1answer
128 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 ...
0
votes
1answer
470 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
264 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
44 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
20 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 ...
0
votes
1answer
143 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
votes
3answers
60 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
0answers
59 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
15 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 $\phi \in V^{*} \text{ \ } \{0 \}$ ...
1
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0answers
13 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
votes
2answers
125 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 ...
1
vote
2answers
53 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.
5
votes
1answer
1k views

Find linear transformation given kernel

Find linear transformation $F$ in canonical bases given $ F: \Bbb R^4 \to \Bbb R^3 $ $ \ker F=\operatorname{span}\left\{\begin{bmatrix}1\\2\\3\\4\end{bmatrix}, \begin{bmatrix}0\\1\\1\\1\end{bmatrix} ...
1
vote
1answer
231 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
478 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
87 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 ...
0
votes
1answer
33 views

Linear transformation from $R^2$ to $R^2$.

Let $\vec{f}: \mathbb{R}^2 \rightarrow \mathbb{R}^2$, where $\vec{f} (\vec{x}) = (x+y^2, x^3+5y)$ and $\vec{x} = (x,y) \in \mathbb{R}^2$. Let $\vec{h} = (h_1, h_2)$ and $\vec{a} = (1,1) \in ...
1
vote
1answer
15 views

Transformation and properties of matrices

If $T:\mathbb{R}^n \rightarrow \mathbb{R}^m$ is a matrix transformation, does $T$ depend on the dimensions of $\mathbb{R}$? i.e., is $T$ one-one if $m>n$, $m=n$, or $n>m$? Also, say if $T$ is ...
0
votes
1answer
56 views

Matrix Transformation - Using matrix multiplication

How do I use matrix multiplication to find the reflection of (-1,2) about the x axis, y axis and the line y=x?
3
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1answer
87 views

Do we lose everything, if the natural transformations in a monad are exactly inverse?

I'm currently explaining monads $$T:{\bf C}\to{\bf C},\hspace{1cm}\eta:1_{\bf C}\to T,\hspace{1cm}\mu:T\circ T\to T,$$ to my brain and the "only" tricky thing are really the identity relations. I ...
0
votes
1answer
2k views

Transformation of ellipsoid to sphere

So I need to find an volume-preservating mapping from an ellipsoid to a ball (solid sphere). (Specifically: x^2/9 + y^2 + z^2 <= 3, but I'd rather understand the general case than just get how to ...
2
votes
2answers
357 views

Transformation matrix from quadrilateral to rectangle

There exists a rectangle somewhere in space with some orientation. A camera from the coordinate center point is looking along the z axis and is seeing the rectangle as a quadrilateral (due to ...
1
vote
1answer
61 views

Transformation Matrix $M_B^B$ of $P_3$ for $B = (1,x,x^2,x^3)$. Is that correct?

I have the following task and just wanted to check weather this is (written) correct(ly). Let $V$ be the vector space of all polynomials of grade $\le 3$ and $f: V \rightarrow V, p \rightarrow p'$ an ...
0
votes
1answer
31 views

Image of $\phi: \mathbb{Q}^{2\times 2} \rightarrow \mathbb{Q}^{2\times 2}, \ A \rightarrow A + A^t$

This question is related to the question I previously asked: Kernel. The following function is given: $$\phi: \mathbb{Q}^{2\times 2} \rightarrow \mathbb{Q}^{2\times 2}, \ A \rightarrow A + A^t$$ ...
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3answers
52 views

Help on finding eigenvalues of transformation on matrices

T is linear transformation working on 2x2 matrices: T(A) = $\begin{bmatrix}1 & 1\\1 &1\end{bmatrix}$ A as far as I see only 0 is an eigen value but someone told me 2 is eigen value too and ...
0
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2answers
78 views

Nilpotent Mappings

Got completely confused with this nilpotent and JCF stuff, need some help. Matrix $A_{n\times n}$ is nilpotent of order K, $1\le k\le 4$ Need to find: a list of all possible dimensions of ...
0
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1answer
205 views

Take -log of a Beta distributed R.V.

X1.....Xn~Beta(a,1) Y = -log(X) Use the transformation formula to calculate the pdf of Y. What named distribution does it have? I am confused what method to use here. A beta does not converge to a ...
0
votes
1answer
10 views

Regarding some elementary transformations

I was trying to follow a math forum thread when suddenly I stumbled upon a transformation that I just couldn't understand. It goes as follows: $v = \sqrt{ 2 U / r - 2 U / r_0}$ $v = \frac{dr}{dt} = ...
5
votes
3answers
95 views

I'm looking for the name of a transform that does the following (example images included)

I'm in the usual situation that if I would know what the name of the thing was, then I could find the answer. Since I dont know the name, here is what I'm looking for: Suppose I have the following ...
2
votes
2answers
400 views

Isomorphism between symmetric and upper triangular matrices

Question: Determine if the vector spaces $V=S_{3}$, the 3x3 symmetric matrices, and $W=U_{3}$, the 3x3 upper triangular matrices, are isomorphic. If they are, give an explicit isomorphism $T: V ...
5
votes
2answers
165 views

What does the Yoneda lemma say for the identity functor and finite sets?

So I try to plug in the simplest arguments into the Yoneda lemma and see how to interpret it. I'll try it for the identity functor and the category of finite sets, in particular, I use an three ...
1
vote
1answer
188 views

Linear Transformation from $\alpha$ to $\beta$

T: $R^3$ $\to$ $R^2$ $$[T]_{\beta\alpha} = \begin{matrix} 2 & 3 & 1 \\ 1 & 2 & 1 \\ \end{matrix} $$ $\alpha$ = {(1, -1, 1), (0, 1, 0), (1, 0, 0)} ...
1
vote
1answer
80 views

Complex Transformation

$z_1 = 1 + i$ and $z_2 = -1 + i$ I am told: $w = \dfrac{az + b}{z + d}$ where $z \not= -d$ Where a, b and d are complex numbers, maps the complex number $z$ onto the complex number $w$. Given that ...
1
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0answers
46 views

Manipulating this probability distribution function

I have a probability distribution function as follows: $$ P(y|x,w, \phi) = \frac{\phi}{2\pi} \exp ^{-0.5 (y-t(x, w)'\phi (y-t(x,w)) } $$ Here $y$ and $x$ are two observed values. $\phi$ is also some ...
0
votes
1answer
42 views

$3D$ projection onto a plane

I have an engineering problem involving math so I figured I ask it here. I have two sets of data: Acceleration in $3$ dimension is given by $\langle X,Y,Z \rangle $. Change of orientation along ...
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vote
1answer
1k views

How can I transform coordinate systems with quaternions?

I have a coordinate system $0$ which I'd first like to rotate about its $z$-axis which gives me system $1$, and afterwards rotate system $1$ about its $y$-axis which gives me system $2$. See picture: ...
0
votes
2answers
148 views

How can I calculate the origin of a scale transformation, given the starting and ending coords and dimensions?

Background: I have two sets of coordinates/dimensions. One for the red rectangle and one for the blue rectangle, as shown below. The blue rectangle is quite simply the red rectangle transformed by ...
0
votes
3answers
144 views

Composite linear map Rank and Image

I have been pondering on this question, I did part $(a)$ wherein you had to prove that $\operatorname{Im}(T)= \operatorname{Im}(T^{2})$ , but I am struggling to get the concept of part $(b)$, any help ...
3
votes
2answers
72 views

Characteristic polynomial of a mapping from matrices space to matrices space

Let $T$ be the linear map from $M_n \to M_n$ given by TX=AX, while A is as well a matrix $n \times n$ (a) Write out the characteristic polynomials for $T$ (b) Show that if A is ...
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vote
1answer
148 views

Transfer Transformation from Physics to Vector Graphic

Upfront, I am not a professional in Maths and hope that the formulation of my question describes the problem well enough. I am creating a jump'n'run game, which uses a physics engine (Box2D) and SVG ...
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vote
3answers
52 views

$T:V \rightarrow V$ And $U \cap Ker(T)={0}$ prove that if$ (u_1,..u_n)$ linear Independent so does $T(u_1)…T(u_n)$

There will be $T:V \rightarrow V $ Linear Transformation U is sub-space of V so that $U \cap Ker(T)={0}$ Prove that if $(u_1,u_2,...,u_n)$ are linear independent so does $T(u_1),T(u_2),...,T(u_n)$. ...
2
votes
2answers
55 views

upper bound for equation

Let $0 < p < 1$ be some constant. I am looking for an $M$ such that $$f(n) = \left(1-p^{\log{n}}\right)^{n} < M(n)$$ I am looking for a tight bound, something of the form: $2^{-n/\log{ ...
1
vote
2answers
133 views

Existence of a linear transformation in an infinite dimension vector space.

If $V$ and $W$ are vector spaces, $\beta=\{v_1, \ldots , v_n\}$ is a finite a basis for $V$ and $\{w_1, \ldots , w_n\}\subset W$, we know there is an unique linear transformation $T:V\rightarrow W$ ...
1
vote
1answer
457 views

Expectation of (1/x)-1 possible transformation involved??

I'm a bit confused with the first steps in this problem: $F(x)=x^4$ for $0<x<1$ a) Find $E[(1/X)-1]$ b) Let $Y=(1/X)-1$. Find the support of $Y$, its pdf and CDF. Name its ...
4
votes
0answers
63 views

Transform recurrence relation

Is it possible to transform following recurrence relation $a_n=4a_{n-2}-a_{n-4}$, $a_0=1$, $a_1=0$, $a_2=3$, $a_3=0$ so that it will have nonnegative coefficients? Number of terms, of course, can be ...
0
votes
1answer
26 views

general rotations

Let $R$ be the rotation about the point $(1,0)$ by an angle of $45$ degrees. By using matrix methods: Find the image of the line $2x-3y+1=0$ under $R$ I would really appreciate it if someone ...
4
votes
1answer
2k views

How can I combine affine transformations into one matrix?

So from what I understand from this picture, the box is stretched to twice its width. And it is then flipped from the x-axis. And then it is rotated 30 degrees anticlockwise. So these three ...
0
votes
1answer
1k views

Find 2D affine transform matrix given a pair of points

I have the coordinates of two points in an initial 2d coordinate system and the corresponding coordinates in a target system. Is is possible to determine the affine transform matrix from these values? ...