# Questions tagged [transformation]

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), (rigid-transformations).

2,246 questions
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### Estimation / Calibration of Transformation of 2DOF laser pointing system in 3D space

Im creating a system where a Laser pointer should be able to point to various objects to direct a certain workflow. This laser pointer has two degrees of freedom, rotations about the local X and Y ...
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### Transforming inequalities [on hold]

Can someone explain to me how to transform it $\left( \frac{en}{s} \right)^{s} \le \left( \frac{en}{s+1} \right)^{s+1}(s+1)(n-s+1)$ to $\left( \frac{s+1}{s} \right)^{s} \le en(n-s+1)$
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### Nonlinear transformation of region from $\mathbb R^2\to\mathbb R^2$

If I have a given continuous nonlinear map $T:\mathbb{R}^2\rightarrow \mathbb{R}^2$, and a region $D \subset \mathbb{R}^2$, is it necessarily true that $T(\partial D)=\partial T(D)$? That is, do ...
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### Modeling the relationship between dilations and area?

On a rather basic high school level I want my students to understand the relationship between the scale factor of a dilation and the area of the pre-image and image. For instance if a rectangle has a ...
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### Galilean transformation and differentiation

Given $x=x’-vt$ and $t=t’$, why is $\frac{\partial t}{\partial x’}=0$ instead of $1/v$? Maybe the answer has something to do with the fact that $dx’=dx$ in this Galilean transformation. Is $dx’=dx$ ...
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### Matrix Transformation for 2D, how do I tell what this matrix does geometrically?

Given a 2x2 matrix, $$\begin{bmatrix}1&-1\\-1&\frac12\end{bmatrix}$$ What geometric effect does it have? So a way I did to solve this was to simply apply it to a unit square that I drew on a ...
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### Does a Bijective Commutative transformation on a vector of angles exist?

I have a problem where I have two vectors a and b representing a list of angles. I need to find a transformation T where T(a,b) = T(b,a), where T has a distance metric to compare two transformations,...
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### Changing rotation center

Things that we have: 2 dimensions, a object with it's coordinates (object P1), it's rotation center (pivot) C1. After that lets rotate it at pivot C1 by known angle A. Now let's move that pivot by ...
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### Transform an Inertia Tensor

I am trying to provide colleagues with a spreadsheet method of transforming the inertia properties of a complex shaped body to a different coordinate system, involving only rotation. I've read that ...
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### Prove that General Affine Transformations preserve ratios of lengths

Let $A$ be a matrix with determinant 1. Then we call a general affine transformation, a transformation of the form \begin{align*} \begin{bmatrix}x'\\y'\end{bmatrix}=A\begin{bmatrix}x\\y\end{bmatrix}+\...
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### Mathematical Source for an algorithm that turns vector to euler angles

Am using the algorithm described here (https://stackoverflow.com/questions/21622956/how-to-convert-direction-vector-to-euler-angles) in the first answer for a thesis in software development. I do ...
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### Transformation of RV: Finding PDF

I am trying to work through this example problem in my textbook but I keep getting the wrong final answer. My Notation: PDF X : pX(x) CDF X : FX(x) Question: Consider the transform Y=X2 if pX(x) = o....
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### Question about group of automorphism of some $G$-structure.

I'm reading Kobayashi's book Transformation Groups in Differential Geometry and I don't understand a thing at page 15. I don't understand why $U$ consists of transformation $a$ of $M$ that leave each ...
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### Pdf of $\sin X$ when $X$ has the pdf $f(x)=\frac{2x}{\pi^2}1_{0<x<\pi}$

I would like to find the PDF of the random variable $Y=\sin(X)$ given the PDF of $X$: $$f(x) = \frac{2x}{\pi^2} \text{ for } 0<x<\pi \text{ and } 0 \text{ otherwise}$$ Following the tips in ...
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### Algebraic transformation — where is my mistake?

I tried to find the estimators of $\hat{\beta_1}$ and $\hat{\beta_0}$ via the least-squares method algebraically. Somehow I seem to have messed up. Can you tell me where? My Calculations.
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### Continuous automorphism of a lie group in kobayashi's book

I'm reading Kobayashi's book Transformation Groups in Differential Geometry and i dont understand a thing at page 14. My question is why $A_\varphi$ is continuous? $G$ is a subgroup of ...
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### Mapping $\Bbb N\to\Bbb Q$

I want to set up a map from $\Bbb N\to\Bbb Q.$ Take $\Phi_S(x)=e^{(S/\ln(1-x))}$ and $M_T(1-x)=\Phi_S(x); S,T\in\Bbb N.$ Set $\Phi_S(x)=M_T(x)$ to obtain algebraic $x$ coordinates. If $x$ happens ...
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### How to solve this problem raven matrices problem?

I am doing this free test in http://test.mensa.no/ That, as far as I know, the only problem I can't solve. Basically we shift the first row to the right. From first to second is easy transformation. ...
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### Matrix transformations.

I am currently learning matrix transformations and ran in to an exercise that I can't understand. We start with e1 = (1,0) e2 = (0,1) So the first transformation is a shear one where e2 becomes -2e1 + ...
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### 3D Vector Rotation Matrix with Radians

I have been working on a simple C++ vector library and needed 3D rotation so I found these 3D rotation matrices on Stack Overflow: ...
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### Finding the pdf of $f(x,y) = e^{-x-y}$ where $Z = X+Y$

I am having trouble understanding how to find the pdf $f_Z(z)$ when $f_{X,Y}(x,y) = e^{-x-y}, x,y \space \epsilon(0,\infty)$ where $Z = X+Y$ My approach is that $$x = x, y = z-x$$ so using ...
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### How does squaring give you a monotonic transformation?

Consider the function: $$f(x,y) = \sqrt {xy}$$ Is the function $$f_1(x,y) = x^2 y^2$$ a monotonic transformation of $f$? I remember studying earlier that squaring does not give you a monotonic ...
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### Show $f(n)= \frac{ (1-\alpha) a^{n+1} e^{-a}+\alpha b^{n+1} e^{-b} }{ (1-\alpha) a^{n} e^{-a}+\alpha b^{n} e^{-b} }$ is unique for $(\alpha,a,b)$

Suppose we have the following function \begin{align} f(n)= \frac{ (1-\alpha) a^{n+1} e^{-a}+\alpha b^{n+1} e^{-b} }{ (1-\alpha) a^{n} e^{-a}+\alpha b^{n} e^{-b} }, \text{ where }n=0,1,2,3,4, \ldots \...
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### Affine Transformation as Rotation

Im trying to do this textbook question which asks me to "express" a motion T(x) = Ax + b in the form T = Rot(P, $\theta$) (A is the rotation matrix) I know that if I draw the transformation, the ...
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### Pinch transform shapes

I'm looking for an algorithm that can pinches a shape in a way to become pointy on both ends. Like this image, transforming the shape on the left to the right. The result is literally similar to ...
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### How to transform basis functions

I know how to transform the basis if we have two sets of basis vectors. Now in my situation, I have two basis equation and I want to find out the transform between those basis functions. Specifically, ...
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### How to find a 2D coordinate field's corners in a 3D Coordinate field if I have 3x 3D points with 3x2D Points?

In order to solve "this" problem, i have to transform my corner-points from a 2D Space to my 3D Space. But my two coordinate fields are only defined by their relation to each other. They have the ...
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### Transformation Theorem on n-dimensional Sphere

$n \in \mathbb{N},b >0$ Define $S_n$ as the n-dimensional Sphere in $\mathbb{R}^n$. I cannot figure out the appropiate transformation to use the transformation theorem such that the following ...
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### Problem with the basis of a linear transformation

I have this exercise Define and find the expression of the linear transformation Information given: $T : \Bbb R^5\to \Bbb R^4$ Im T = ⟨(3, -1, 0, ...
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### Mathematical expression as LP problem

I am seeking for a linear programming expression for the following expression: enter image description here B(x) is the neighborhod of f(y) (where delta is the size of the neighborhod). It can be an ...