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).

2,310 questions
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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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Fundamental Theorem of Calculus with Inverse function. Explanation, intution and proof please

I'm an undergraduate student studying for the actuarial exams and was wondering if someone could please walk me through the proof and intuition of this please? I haven't taken an analysis course yet, ...
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Forward and Backward Projections

I have the transform functions (forward and backward projections) such as: $$FP\{f(x,y)\} = \int_{-\infty}^{\infty}f(r\cos(\theta) - z\sin(\theta), r\sin(\theta) + z\cos(\theta))dz$$ BP\{g_{\theta}(...
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Transformation of Random variable $Y=-2\ln(F(x))$ [closed]
Let $X$ is a continuous Random variable. with strictly increasing function cumulative distribution function $F(x)$. Find and recognise the distribution of random variable $Y=-2\ln(F(x))$. I need some ...