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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Integral transformation

I'm trying to do a transformation of an integration, I have that $$\int_{0.5}^1\int_0^{0.5}e^{xy}xydxdy$$ And I want to get that integrate $$\int_0^1\int_0^1 f(x,y)dxdy$$ Where the value of the ...
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38 views

is it possible to decompose nonperiodic sinusoidal signal?

Using Fourier series we can decompose any any signal into it's elementary signals but condition is that signal should be periodic and sinusoidal one. Now, is it possible to decompose nonperiodic ...
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36 views

Do all n x n matrices over the reals represent linear transformations?

Do all $v \in M_n (\mathbb{R})$ represent linear transformations? To add to that a bit to further clarify for myself: Looking up the def. of a transformation it is any function $f$ mapping a set $X$ ...
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1answer
42 views

When does $ \langle gI, t \rangle = \langle I, g^{-1} t\rangle $ hold true?

Consider $I, t \in \mathbb{R}^d$ and $g$ is some element in a group of transformations (for example like the affine group in $\mathbb{R}^2$). I was wondering when the inner product $ \langle gI, t ...
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116 views

Fourier Decompositon problem

have a look at this video of Fourier Decomposition of an image (otherwise you can also refer the image, which shows few plots of different extracted waves from an image). We also know that a Fourier ...
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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 $T( \overrightarrow{x} )=A\overrightarrow{x}$, ...
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Can someone explain this z transformation to me?

I have a signal $h[n]=\frac{1}{z+3}$ and the solution is $H(z) = (-3)^{n-1}\delta[n-1]$. Looking the solution up in a transformation table, I come to the conclusion that I need to transform $h[n]$ ...
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21 views

About the proof of Zeta Transform

I have to prove $$Z[k^n]=(-1)^nD^n\left(\frac{z}{z-1}\right)$$ where $$D=z\frac{d}{dz}$$ and $n$ varies over the set $\mathbb{Z}$ My book doesn't give me any advice; how can I go further?
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About the notation in zeta transforms

My book writes: $$Z[n^k]=(-1)^kD^k(\frac{z}{z-1})$$where $D=z\frac{d}{dz}$ and $n$ varies over the set $\mathbb{Z}$. What does $D^k$ mean?
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78 views

Fast Hankel Transform

Can someone please explain what would be the expression for weights(Ho) in a Fast Hankel Transform.I found this in a paper and could not find any satisfactory answers .
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Change of Basis Matrix: Cartesian to Spherical Laplacian

I was looking at how a change of basis matrix, $[P_{\beta\leftarrow\alpha}]$, is made. While this is a bit more advanced that than what was taught at the course, I wonder what would be the change of ...
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Singularities in the Gauss Hypergeometric Function

I am evaluating the following term in a series: $$I_k = \int\!x^{-3(2k+1)}(1+\lambda x^4)^{-1/2}\,\mathrm dx$$ When I plug this into WolframAlpha, I get the following result: $$I_k = ...
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51 views

How to compare ZOH and tustin

I'm discretizing some continuous time systems. Now there (MATLAB) are of course different types of discrtization methods, among them tustin (bilinear), euler backwards, euler forward etc. Often one ...
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33 views

question on Fourier Transformation

I have to find the Fourier Sine transform of $f(x)=1$ when $|x|<a$ and $f(x)=0$ when $|x|\ge a$ and hence show that $$\int_0^\infty {\sin(t)\over t} dt =\pi/2$$ and $$\int_0^\infty ...
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44 views

$K=\frac{1}{2}mV^{2}$, random variable transformation.

An object has random velocity $V$ and kinetic energy $K = \frac12mV^2$, where $m$ is the mass of the object. Suppose that the velocity has the Laplacian distribution with probability density ...
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1answer
69 views

3D rotation of an object with respect to another object's rotation

I am writing a python code to translate and rotate an object with respect to another object. Please take a look at the picture bellow: The smiley face and the arrow have initial poses (position ...
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2answers
50 views

Proof that $V^*$ is isomorphic to $V$.

In my notes for a linear algebra course there is proof that $V^*$ is isomorphic to $V$. However I am unclear on a few of the steps. We begin by choosing a basis $B = \{v_1,...,v_n\}$ for $V$. We now ...
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39 views

transformation of single random variables with absolute value ??

integral I got the final answer to be fy(y)= 1 0< y < 1 I am not sure could anyone correct me if its wrong !
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What are the limitations /shortcomings of Fourier Transform and Fourier Series?

I am fond of Fourier series & Fourier transform. But every approach has some outcomes and some shortcomings. It's limitations lead to innovation of new approach. So, can anybody explain about ...
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1answer
30 views

Confusion with the notation $L_A$

My linear algebra class went from 0-100 real quick. I've attended every single lecture (so I know I haven't missed out on anything); however, very recently he has been using the notation $L_A$ for a ...
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23 views

Remove Multiplicative Constant from Hypergeometric Function

I have a function of the form $$f(x;\lambda) = {}_2F_1\left(a,b;c;-\frac{e^{2x}}{\lambda}\right)$$ I need to invert this function to solve for the constant $\lambda = f\left(x\right)$. I could do ...
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58 views

Transformation to polar coordinates

I know this is very simple and I'm missing something trivial here... I'm having trouble converting this set of equations to polar form: $$ \dot{x_1}=x_2-x_1 (x_1^2+x_2^2-1)\\ \dot{x_2}=-x_1-x_2 ...
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3answers
2k views

Any linear fractional transformation transforming the real axis to itself can be written in terms of reals?

I'm trying to teach myself complex analysis, and was reading about linear transformations. I would like to understand why any linear fractional transformation which transforms the real axis into ...
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87 views

What are Basis images?

I have read that using Fourier transformation we can decompose any arbitrary image into orthogonal basis images and reconstruct it back. But what are basis images actually?
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Have some queries about Fourier Transform

I have some queries about the Fourier transform In most of the cases, the Fourier transform of a signal is symmetric with respect to positive and negative frequency. I think the computational ...
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Find a matrix to represent the mapping of a factor module

I have a problem from my past paper I can't figure the logic to, even after seeing the answers. The question goes 【Q】Let $V=\mathbb{R}[X]_{<4}$ be the vector space of real polynomials of degree ...
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Transformed pde but my answer doesn't match solution?

$$\frac{d^2u}{dx^2} + \frac{d^2u}{dy^2} + \frac{du}{dx} + 2\frac{du}{dy} + 3u = 0$$ Let $u = ve^{ax + by}$ and find $a, b$ such that we can transform to the following equation $$\frac{d^2v}{dx^2} + ...
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106 views

How to determine when this two variable transformation is invertible?

I am given: $$ X= U \cos(V) \tag{1}\\ $$ $$ Y = U \sin V \tag{2}$$ Now, I need to: a) Give the respective ranges for $U$ and $V$ in order that the transformation defined is one to one. and ...
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1answer
24 views

How to go about finding a transformation $T$ in order to solve an integral.

I have the integral $$\int\int_R\left(2x+y\right)dA$$ Where $R$ is the region bounded by $$x+y=-1, x+y = 3, 2x=y,2x-4=y$$ So my first though was drawing the region, which gave me this odd region, so ...
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Projective transformation a parabola to a circle

Take the parabola $x^2 - y = 0$ in the cartesian plane. I'm not entirely sure about this, but we can express this using homogenous coordinates as $X^2 - Y = 0$ (the $W$ coefficient is $0$?) With the ...
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transform orthonormal coordinate system to another

I have one orthonormal coordinate system ABC that it's origin is the point p0. I would like to transform it to another orthonormal coordinate system A'B'C', that it's origin is p1. I know how to ...
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Eliminating 3rd term in $\frac{d^2u}{dx^2} + \frac{d^2u}{dy^2} + 3u = 0$ through change of variables?

I want to eliminate the third term in this pde $$\frac{d^2u}{dx^2} + \frac{d^2u}{dy^2} + 3u = 0$$ Here's what I thought of, is this ok? Let $a = \lim \limits_{k \to \infty} kx$ Let $b = \lim ...
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Show whether this linear transformation is one-to-one and onto.

$T:P_2$ $\rightarrow$ $R^3$ is a linear transformation defined by $$T(a+bx+cx^2) = \left[ \begin{array}{ccc} 2a-b \\ a+b-3c \\ c-a \end{array} \right]$$ This linear transformation is neither ...
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112 views

Whether the job of Fourier Transform is just to convert signals from time domain to frequency domain only or more than it?

I am a beginner . We convert a signal in time domain to frequency domain by applying Fourier transform on the signal to obtain frequency and phase spectrum. So,whether the job of Fourier transform ...
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1answer
19 views

Transforming pde to nicer form?

I have a second order differential equation for $u$ $$\frac{d^2u}{dx^2} + \frac{d^2u}{dy^2} + 5u = 0$$ I am looking for a transformation $u(x,y) \rightarrow v(x,y)$ that gives $$\frac{d^2v}{dx^2} + ...
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Converting fractional coordinates to cartesian coordinates

I have a set of fractional coordinates with the following vectors: 2.950 -1.475 0.0000 0.000 2.5547 0.0000 0.000 0.0000 77.5379 with the ...
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65 views

Proof that Determinant is Scale Factor

I've seen a lot of supposed properties of linear transformations that're never proven -- just often repeated. These include: The determinant is the scale factor between the volume of region in your ...
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Education tool for learning 3D angles

I hope it is not an off-topic. I have started working on 3D frame transformation and transforming a vector such as acceleration or angular velocity from one coordination to earth coordination. My ...
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40 views

transforming $(A,B,C)$ to $(0, 0, 1)$ by rotations

I'm trying to reflect the "world" through a specified plane $p:Ax+By+Cz=0$. I know how to reflect the "world" through the $xy$-plane, so I want to rotate $p$ in the $3$ axes ($x,y,z$-axes) so it will ...
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1answer
41 views

Lens Conformal Map

Please help me find a conformal map of the set $ A = \left \{\; z: \; |z-1| < \sqrt{2} \; and \; |z+1| < \sqrt{2} \; \right \}$ one-to-one onto the open first quadrant. First, I noticed that ...
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1answer
24 views

Distribution of Logistic of Normal

If $X \sim N(\mu_X, \sigma^2_X)$ and $Y= \frac{\exp(X)}{1+\exp(X)} $, what is the distribution of $Y$? I thought logit-normal would fit the bill, however the logit of $Y$ is ...
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Transformation of a Partial Differential Equation

How can we convert $$\frac{\partial c}{\partial t} = M\left[\frac{\partial}{\partial x}\left(c\frac{\partial c}{\partial x}\right)+\frac{\partial }{\partial y}\left(c\frac{\partial c}{\partial ...
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Proving a theorem on a rotation about a line followed by the inversion to show that it is a reflection

A theorem in my textbook is : A rotation about a line followed by the inversion about a point on that line is a reflection or a rotary reflection. I can picture this theorem in my head on a 3D space ...
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41 views

Rotation in high dimension in the direction of given vectors

Given two vectors $A$ and $B$ (with high dimension), and an angle $\alpha$. How can one find the vector $C$ which is $A$ rotated over $\alpha$ in the direction of $B$? If it changes anything: the ...
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Transforming coordinates according to Point of View.

Imagine I have two cameras (A and B) in the same axis and looking at the same white wall with a black dot. Both cameras see the black dot. I'd like to know how to proceed in order to derive the black ...
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Dynamical System transformation

How can the system $$\frac{dx}{dt}=-y+\epsilon x(x^2+y^2)$$$$\frac{dy}{ dt}=x+\epsilon y(x^2+y^2)$$ be transformed into $$\frac{dr}{dt}=\epsilon r^3$$ $$\frac{d\theta}{dt}=1$$ via polar coordinates? ...
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1answer
72 views

How do i scale 2D vector using matrix

I know that scale matrix is 2x2 { x, 0, 0, y } basis. My vector { 100, 2 } and i want to scale it using custom 2x2 matrix. I've read that if left operand is 2D row vector, then multiplying it on a ...
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Elementary Transformation of Mean density

Sir Im confused about dealing with some transformed mean density. I cant follow the logic how the author derived a specific result out from the following given: $$p(t) = \frac{1}{nπ} ...
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transformation of mean density

Sir Im confused about dealing with some transformed mean density. I cant follow the logic how the author derived a specific result out from the following given: $$p(t) = \frac{1}{nπ} ...