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10 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 ...
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0answers
7 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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1answer
268 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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0answers
11 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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2answers
13 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
33 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
30 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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0answers
25 views

What exactly is a transformation matrix with respect to a basis?

Say we have a linear transformation $T(V,W)$. Let $\{v_1,v_2,\dots,v_m\}$ and $\{w_1,w_2,\dots,w_n\}$ be the bases of $V$ and $W$ respectively. Then $T(v_i)=\sum\limits_{k=1}^n{a_{k,i}w_k}$. I ...
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1answer
19 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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0answers
27 views

Composite transformation expressed as a single transformation

Question: Working: Q 0.9 O r 5.3 = Q 0.9-5.3/2 = Q -1.75 Based on the question, it seems that I have to add pi to -1.75 which gives *Q*1.3915 Is my answer correct? And ...
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0answers
22 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 ...
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1answer
1k 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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2answers
31 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
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1answer
25 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
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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 ...
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1answer
14 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?
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0answers
11 views

Inverse coordinates on a matrix

I am trying to "inverse" some coordinates on a matrix. For example, take this grid: ...
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1answer
57 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 ...
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1answer
28 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 ...
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1answer
28 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 ...
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0answers
5 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 ...
2
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2answers
212 views

Find the matrix A of the linear transformation T(M)

I know that if I substitute the first matrix for $T(M)$ I see what T does to each of the basis vectors. I don't understand how that creates a $3\times 3$ matrix though. I was looking at this ...
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1answer
2k views

Find the Matrix A of the Linear Transformation

Can anyone walk me through the steps to complete this problem? I am unsure of where to start to solve the problem. I get that the resulting matrix $A$ should be a $2 \times2$ matrix, should I be ...
0
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1answer
23 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
36 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 ...
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2answers
56 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 ...
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1answer
20 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
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1answer
9 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} = ...
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3answers
60 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 ...
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0answers
24 views

Fourier Transform, Geophysics, Signal Analysis

Geophysics question I don't know if i'm over simplifying it but it says $$ \omega_0 = 2\pi f_0 $$ where $$f_0 = 1/2\pi $$ because that's the frequency of cosine? And that'd just make $\omega_0 = 1$. ...
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2answers
104 views

Transformation between the same rotation expressed in different coordinate systems

EDIT Lets assume my transformation does the following mapping: x = -y y = -x z = -z Which produces this transformation matrix $R_t$: $ \begin{array}{lll} 0 & -1 & 0 \\ -1 & 0 & 0 \\ ...
2
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2answers
61 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 ...
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2answers
97 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
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1answer
32 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
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1answer
19 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 ...
2
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1answer
1k 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. ...
2
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1answer
215 views

Exponential Function Shifts

I have some confusion about shifts concerning exponential functions. I can best describe my question with an example. Take y = e^-(x-3). This graph has a reflection over the y-axis and is shifted ...
5
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1answer
119 views

Jacobian of Fourier Transformation

I am trying to calculate the Jacobian determinate of the Fourier transform which I stumbled upon when studying the Path Integral in Quantum Field Theory. I know the answer should be $1$ but I don't ...
1
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0answers
18 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
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1answer
17 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: Both ...
0
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1answer
24 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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1answer
226 views

Understanding perspective transform matrix elements interpretation

I am representing 3D points (vectors) in the following way: ...
0
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1answer
14 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 ...
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3answers
25 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 ...
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2answers
50 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 ...
1
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1answer
40 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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3answers
22 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 $T(u_1),T(u_2),...,T(u_n)$. ...
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2answers
42 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{ ...
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2answers
44 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 $T:V\rightarrow W$ ...
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2answers
160 views

Consider the trace map $M_n (\mathbb{R}) \to \mathbb{R}$. What is its kernel?

The map is the trace map. I.e, it takes any $n$ by $n$ matrix and associates to that matrix, a number of the form $\mathrm{Tr}(A) = \sum_{i=1}^n a_{ii}$, where $A \in M_n (\mathbb{R})$. I need to ...