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0
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2answers
70 views

Number mapping function

I can't find out a function f(x)=y that would map my x's to required y's. It is OK to write it in a programming language. Notation in mathematics is also OK. It ...
3
votes
1answer
351 views

Translation Matrix and Why non linear?

When we translate a point $p_3 = (x,y,z)$ to coordinates $p_4 =(x + t_x , y + t_y ,z + t_z,1)$ we use $4 \times 4$ Translation matrix using homogenous coordinates, hence we add a $1$ to fourth ...
1
vote
1answer
117 views

Derive Rigid Transform Matrix from Axes and Origin

I'm trying to derive the matrix of a rigid transform to map between two coordinate spaces. I have the origin and the axis directions of the target coordinate space in terms of the known coordinate ...
1
vote
1answer
103 views

Discover matrix of linear transformation between non-canonical bases

I'm solving a linear algebra problem. I have linear transformation $D$: $D : R_2[t] \rightarrow R_2[t]$ $D(p) = \frac{d}{dt}p$ and bases: $A = \{1 + t, 1- t, t^2\}$ $B = \{1 + t, 1 - t\}$ Now I ...
1
vote
1answer
65 views

Correlated Equilibrium - Transforming a non-linear objective function into a linear one

I am trying to transform a non-linear objective function into a linear one, in order to create a LP. How might I go about to do this (I have never taken a course in linear programming). I have that I ...
0
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3answers
227 views

$f: V \mapsto V$ is a projection, show $V = \ker(\pi) \oplus \operatorname{Im}(\pi)$ [duplicate]

Possible Duplicate: Show that $V = \mbox{ker}(f) \oplus \mbox{im}(f)$ for a linear map with $f \circ f = f$ I think I need to use the fact that if $v \in V$, then $v = (v - \pi(v)) + ...
1
vote
3answers
189 views

Pre–emphasis - Signal Processing

I am trying to compute the Pre-emphasis of a signal and the formular is below: y[n] = x[n] - 0.95 x[n-1] Let: ...
2
votes
1answer
54 views

Need an explanation of a particular expression transformation

Please, I need an explanation of the one transformation. I have the equation set and its solution. $$ \begin{cases} \frac{x}{y} + \frac{y}{z} + \frac{z}{x} = 3\\\\ \frac{y}{x} + \frac{z}{y} + ...
0
votes
0answers
202 views

Girsanov Transformation Example

Is this the correct use of Girsanov's transformation where $B_{n}$ is a discrete Brownian motion? For example computing: $E[(B_{n}+2n)^{2}]$ Set: $\widetilde{B_{n}}=B_{n}+2n$ And ...
1
vote
0answers
17 views

Need help transforming an list of numbers into some uniform list in order to apply the rule mentioned inside more effectively

So I have a list of values like so L1 = [-4 -3 5 8 ]; Note the sum of each element in L1 will always be > 0. The operation I am performing on L1 is as follows ...
1
vote
1answer
202 views

Subspaces, transformation matrices exercise

I have trouble understanding the following exercise so I would really appreciate any help you could give me: Let $k$ be a non zero vector in $\mathbb R^n$, written in standard basis. Let $H$ be ...
17
votes
1answer
269 views

Show that $\phi: \mathbb{R}_3[x]\rightarrow\mathbb{R}^3, \phi(p):=[p(-1), p(0), p(1)] $ is a linear transformation

Let $\mathbb{R}_3[x]$ be a vector space of polynomials p with degree $\leq3$ and show that $\phi: \mathbb{R}_3[x]\rightarrow\mathbb{R}^3, \phi(p):=[p(-1), p(0), p(1)] $ is a linear transformation. ...
1
vote
1answer
470 views

Finding a 3D transformation matrix based on the 2D coordinates

I have a square with the length of the sides being 1. This square is transformed by an unknown transformation matrix in the 3D space and then projected back to the plane (the projection is known). I ...
0
votes
1answer
122 views

Changing Frequency of a Fourier Transformed signal

How can I change the frequency of a signal after taking its fourier transform? I am taking voice input from user in MATLAB and than I take its fourier transform to convert the signal in frequency ...
0
votes
1answer
227 views

What are spatial Transformations?

What are spatial Transformations? Are Affine transformations also part of spatial transformations?
0
votes
2answers
221 views

Fourier Transformation

This expression: $x(t)=[e^{-3t+5}] u(t-1)$. I am trying to take the Fourier transformation of the above expression. I know that for $x(t)=[e^{-at}] u(t) \leftrightarrow \frac1{i\omega+a}$. But, ...
0
votes
1answer
54 views

Proof Correctness: $T \in L(V,V), T^2 = 0 \iff T(v) \subset n(T)$

Prove: $T \in L(V,V), T^2 = 0 \iff T(v) \subset n(T)$ Is the following correct? Proof: $\rightarrow$ Let $T^2 = 0 \iff T(T(v)) = 0$ Suppose $x \in T(v)$ we must show that $x \in n(T) \iff T(x) = ...
0
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3answers
5k views

Image and Kernel of a Matrix Transformation

So I had a couple of questions about a matrix problem. What I'm given is... Consider a linear transformation $T: \mathbb R^5 \to \mathbb R^4$ defined by $T( \overrightarrow{x} )=A\overrightarrow{x}$, ...
2
votes
1answer
100 views

Find rotation that maps a point to its target

I have a 3D point that is rotated about the $x$-axis and after that about the $y$-axis. I know the result of this transformation. Is there an analytical way to compute the rotation angles? $$ ...
1
vote
1answer
387 views

What is the Matrix corresponding to a Linear Transformation

Given $T: P_2 \rightarrow P_3$ defined by: $T(at^2 + bt +c) = (a-b+c)t^3 + (-a + 3b - 2c)t^2 +(-a-b)t +(2b-c)$ What is the corresponding Matrix of $T$? This is what I have: First I rewrite the ...
0
votes
1answer
101 views

Legendre transform of log moment function

Here is something I do not understand for my lecture notes. The lemma is this. Let $\mu$ be a probability measure on $R$, and $\Lambda^*_\mu$ is the Legendre transform of $\mu$. $\Lambda_\mu^*\geq ...
2
votes
1answer
151 views

Find basis for $\ker T$ with $T:P_2 \to P_2: T(p(x)) = p(x) + p(-x)$

$T: P_2 \to P_2$ defined by $T(p(x)) = p(x) + p(-x)$. Find basis for $\ker T$ Here is my solution: $$p(x) = ax^2 + bx + c$$ $$p(x) + p(-x) = 0 \to 2ax^2+2c =0$$ So, a = c = 0. So, basis of $\ker T$ ...
0
votes
1answer
100 views

Basic Math: Simplifying $w=z^2+3z$

The question is: Consider the transformation $$w=z^2+3z$$ from the $z$-plane where $z=x+iy$ and $w=u+iv$. Determine the image of the line $y=1$ and $x=3$ in the $w$-plane My attempt at a solution: ...
2
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0answers
59 views

bound on Hilbert transform

Consider $\widehat{Tf(\xi)}=m(\xi)\hat{f}(\xi)$, where $m(\xi)=(1-\vert\xi\vert)1_{[-1,1]}$, i.e. $T$ is the operation of taking Fourier transform and multiplying with the function $m(\xi)$. I am ...
2
votes
1answer
194 views

Linear Algebra Question ( rank of matrix )

Let $\bf A$ be an $m \times n$ matrix. If $\bf P$ and $\bf Q$ are invertible $m \times m$ and $n \times n$ matrices, respectively prove $\operatorname{rank}(\mathbf{PA}) = ...
0
votes
1answer
87 views

Linear transformations and range

Let $A$ be an $m \times n$ matrix. Suppose that the matrix equation $AX = Y$ is consistent for any $Y$ that is an element of $R^m$ . (a) What is the range of $T_A$? Justify your answer. (b) Under the ...
1
vote
1answer
160 views

How to solve/transform/simplify an equation by a simple algorithm?

MathePower provides an form. There you can input a formula (1st input field) and a variable to release (2nd input field) and it will output a simplified version of that formula. I want to write a ...
1
vote
1answer
102 views

Creating a 3D surface from 2D graphs

So I have two sets of equations: $\mathcal{A}$ = \begin{equation} \{ f(y_{0},x), \, f(y_{1},x) , \;... \;, f(y_{n},x) \} \end{equation} $\mathcal{B}$ = \begin{equation} \{ g(y,x_{0}), ...
2
votes
2answers
47 views

Scaling range of $n$ numbers to $m$ numbers

I have $n$ values ($n \approx 10^8$) ... I want to plot these, where the $i$-th value is plotted at point $(x,y)$, $x=i$ and $y=$value$[i]$. Note: The values do NOT follow any pattern or function. ...
4
votes
2answers
301 views

How to solve an overdetermined system of point mappings via rotation and translation

I have a set of points in one coordinate system $P_1, \ldots, P_n$ and their corresponding points in another coordinate system $Q_1, \ldots , Q_n$. All points are in $\mathbb{R}^3$. I'm looking for a ...
1
vote
1answer
39 views

Multi 3D Screen to POV

See, im a simple hardcore Programmer. In fact i wrote some 3D-Programs till now. I had nothing to do this weekend, so i made a 3D-based filemanager. My desktop is multihead so the point-of-view of ...
2
votes
1answer
146 views

Reflecting an exponential function over a y = 3 line.

How would you write the equation of $f(x) = 4^x$ that reflects over the line $y = 3$? I've put in $f(x) = 3 + 4^{-x}$ which I thought was the right answer, but it isn't. Thanks in advance!
1
vote
1answer
115 views

Transformation of Quadric Surfaces

Is there a transformation $T: \mathbb{R}^3 \longrightarrow \mathbb{R}^3$ such that a hyperboloid of one-sheet can be mapped to a hyperboloid of two-sheets using such transformation?
0
votes
2answers
58 views

Multivariate Random Variables

$f(x,y) = {2\over 5}(2x+3y) \quad for\quad 0<x,y<1 $ and we want to know the distribution of $2X+3Y$ I did it in a very lousy way which is let $ U=2X+3Y ,\; V=X$ Then have $\;f_{U,V}(u,v)$ ...
0
votes
1answer
285 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 ...
4
votes
1answer
108 views

How do you create a “stretch” transformation while keeping volume constant?

A stretch transformation can be represented as: $$ \begin{bmatrix} k & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix} $$ However, this changes the volume of any object which ...
2
votes
0answers
204 views

Understanding Discrete Cosine Transformation

I'm currently working on some software and a key component is 2D DCT. But my question is more general, as I'm trying to understand the DCT in general, let's say from engineers point of view. For ...
0
votes
2answers
136 views

Map 2D points inside a closed curve to unit disk

Hy everyone, I have a set of 2D cartesian points (x,y coordinates) lying inside an arbitrary closed contour , something like this: arbitrary_closed_contour by 'arbitrary' I mean that the closed ...
0
votes
1answer
332 views

Composite transformation expresing as single transformation

This is the composite transorfmation that I have this is the working that I did, but something tells me this might not be the right answer, P.S can some with more points add composite ...
0
votes
0answers
85 views

Riccati equation transformation

Is possible to transform this Riccati equation into a linear differantial one? Thank you. $$ y=y_1+\frac{1}{z} $$
1
vote
1answer
49 views

Coordinate transformation to get even function

Suppose I have the function $$f(y)=2y^4-5y^3+3y^2,$$ with zeroes $y=0$ (2x), $y=1$, $y=3/2$, which I only need on the part of the domain $0\le y\le 1$. Is there a transformation $y\rightarrow y'$, ...
5
votes
2answers
371 views

Are Legendre transforms of non-convex functions useful?

Do Legendre transforms have any applications that do not appeal to convexity? What is the intuitive interpretation of the Legendre transform of a non-convex function?
0
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2answers
2k views

Linear Transformation with 2x2 Matrix Basis

The question asks: Find the "coordinates" of $v=\begin{bmatrix} -2 & -2 \\ -2 & 4 \end{bmatrix}$ relative to the ordered basis, $F=(f_1, f_2, f_3, f_4)$ where $f_1 = \begin{bmatrix} 1 & ...
3
votes
1answer
340 views

Find Möbius transformation that send Re(z)=Im(z) to a circle and the real axis to itself

Problem 3.3.7d in Complex Variables, 2nd edition, by Stephen D. Fisher. Find a linear fractional transformation $T$ that maps the real axis onto itself and the line $y=x$ onto the circle ...
2
votes
1answer
65 views

Semigroup question

I am looking for the technical term for an element of a transformation semigroup that sends everything to one state. The best term I could think up was filter. For those that don't know a ...
0
votes
2answers
177 views

3D transformation between two polylines problem

Say I have 2 separate objects. One is a line defined by two points, the other is a polyline defined by three points. Line 1 consists of the set of two points: $a=(0,0,0)$ and b=$(0,0,1)$ Line 2 ...
3
votes
1answer
569 views

Transformation matrix to go from one vector to another

I've two vectors $a = (a_1, a_2, a_3)$ and $b = (b_1, b_2, b_3)$. How to find transformation matrix for transform from a to b?
1
vote
2answers
722 views

Formula transformation

Is it possible to transform this equation to give R? $$y=x\left[\frac{\left(1+\frac{R}{12}\right)^{12\times{25}}}{\frac{R}{12}}-1\right]$$
0
votes
1answer
2k views

Function transformation order of operations

I am reviewing for a midterm for Pre-Calculus and I am trying to understand the concept of function transformation: Let's say I am given a function $f$ with the domain in the interval of $[1,5]$ and ...
4
votes
1answer
130 views

Is there a geometric argument that the Legendre transform of a convex function is convex?

I am trying to build intuition on Legendre transforms. Arnold's Mathematical Methods of Classical Mechanics has some nice geometric interpretations, but he does not provide a proof that the Legendre ...