# 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).

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### Series expansion involving Kummer and Tricomi functions analogy

Good day to everyone. I've got in a pickle while toying around with some transformations. It is well-known that the bivariate confluent hypergeometric function $\Phi_2(\cdot)$ can be expanded in the ...
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### Find the bilinear transformation which maps z=(1,-i,2) respectively into w=(0,2,i) [closed]

Find the bilinear transformation which maps z=(1,-i,2) respectively into w=(0,2,i)
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Is it possible to combine the rotation and reflection matrix in one matrix? $$Rot(\alpha)=\begin{pmatrix}\cos(\alpha) & -\sin(\alpha)\\\ -\sin(\alpha) & \cos(\alpha)\end{pmatrix}$$ $$Ref(\... 0 votes 0 answers 16 views ### Equivalence with the Weierstrass transform I have the following expression$$\frac{1}{\sqrt{4\pi t}}\int_{-\infty}^{+\infty}dx~ f(x-y) e^{-x^2/4 t} \tag{1},~~\forall ~y \in \mathbb{R}.$$. I am trying to relate it with the generalized ... 5 votes 0 answers 132 views ### How to a^b \to b^a [duplicate] Addition, multiplication and power are formed in a similar way. One follows from the other by repeating the preceding action several times. But while a+b=b+a, and a \times b=b \times a, in turn a^... 2 votes 2 answers 57 views ### Coordinate Transformation of Double Integral Evaluate the integral by making an appropriate change of variables.$$\iint_R\left[\cos \left(\frac{y-x}{y+x}\right)\right]^2 dA$$where R is the trapezoidal region with vertices (2,0), (3,0), (0,3)... 0 votes 0 answers 51 views ### Shape of a transform matrix that maps \mathbb{R}^{a \times b} to \mathbb{R}^{c \times d} I'm looking for the dimension of some tensor T that transforms a \times b matrices to c \times d matrices. I initially thought it would have to be of a greater dimension, perhaps some shape like ... 0 votes 0 answers 38 views ### Is the volume equivalent of every odd dimension conserved after deformations? I don't know the best way to phrase this (english isn't my main language), so I'll do my best. First we have the perimeter (one dimension, a line), which is conserved after a deformation. for example ... 0 votes 1 answer 46 views ### Next Step After Finding Eigenvalues of Transformation Matrix T? I've successfully determined the eigenvalues of the transformation matrix (T = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 5 & -10 \\ 1 & 0 & 2 & 0 \\ 1 & 0 & ... 0 votes 1 answer 28 views ### Lie group of transformations in a plane. I was trying to solve the following problem: Check whether the transformations of the plane given below forms a Lie group.$$x^{*}=x-\varepsilon y;\quad y^{*}=y+\varepsilon xI tried to identify the ... 1 vote 0 answers 111 views ### Proof-Check: Beta-distribution sample generation through variable transformation Purpose of this thread: I want your feedback on my proof for the following problem and correct it where necessary. Problem: For \alpha > 0 and \beta > 0, consider the following accept–reject ... 6 votes 1 answer 131 views ### Is it possible to construct a coordinate system which gets "pulled in" I really hope i can explain our issue adequately and keep this purely math bound, even if it is technically a graphics programming related question. But over on their exchange ill never get an answer. ... 0 votes 0 answers 18 views ### Mixing conditional random variables by sampling I am struggling to put my transformation of data into mathematical contexts. My goal is to define a mapping that transforms the original data into some awkwardly mixed data. In my simulation study, I ... 1 vote 1 answer 39 views ### Finding a transformation that squares the components of a vector I am looking for a transformation (of any type, as long as it can be written mathematically and not semantically) which takes a vector of infinite dimensions to another vector that has components ... 0 votes 0 answers 31 views ### Exact Successor State Distribution for a Pendulum I want to solve the following problem. Suppose we have a simple pendulum, which follows the differential equation \begin{equation} \dot{x} = f(x) = [x_2, -\sin(x_1)]^T, \text{with } x=[x_1, x_2]^T. \... 0 votes 0 answers 24 views ### Effects of horizontal scaling on area under curve? If f(x) is a continuous function and we stretch it horizontally by a factor n (multiply x by 1/n in the formula) then my intuition and some examples i solved tell me that if we look at a segment of ... 0 votes 1 answer 74 views ### Rotation of angle 2k\pi/p generates the group of all rotation In the book Geometric Transformation of Razvan Gelca, there is an argument as follows: I could understand most of the proof there, however is there any easier explanation for the yellow painted part, ... 0 votes 0 answers 17 views ### Dual graph relation to star-mesh duality I'm confused about the realtionship between dual graphs and the so called star-mesh transformation: https://en.wikipedia.org/wiki/Star-mesh_transform. Take a simple triangle, its dual graph looks like ... 0 votes 2 answers 63 views ### Intersection and union under arbitrary function I have tried to grasp topology homeomorphism. I have heard that such transformations preserve intersections and unions. I have tried to prove it myself and it came out that actually any transformation ... 1 vote 1 answer 69 views ### Is there a canonical form for rational expressions? Polynomials have a canonical form \sum a_n x^n which makes it easy to understand what a polynomial is. Yet rational expressions can often wear many disguises, where it's not obvious that two ... 1 vote 0 answers 19 views ### How would I scale up a set of values while preserving their original increasing order using logarithmic functions? I've got a set of data ranging between 0 and 1. Most of the values in this set are extremely small (like, between 0.003 and 10^-7). I want to scale up these values, so they are less small but still ... 0 votes 1 answer 39 views ### Expected value of transformation of exponential PDFs I have the following: X and Y are exponentially distributed with parameter \lambda. They are independent of each other. I also have U = X+Y and V = X-2Y. I am asked to find E(V|U=1). What ... 0 votes 0 answers 23 views ### General exponential grid A known function that maps the interval [-1,1] onto itself that is used to modify a linear gridding into an exponential one is given by, \begin{align*} f \colon [-1,1] &\to [-1,1]\\ x &\... 0 votes 0 answers 18 views ### Transform ratios with negative numerators I am working on a regression model that takes in features that are in the form of ratios. For example, one of the ratios is: ... 1 vote 0 answers 66 views ### What is Meant by "Change of Origin" in Coordinate Geometry? I don't think I understand what is meant by "to shift the origin of coordinates to the point (h,k) in coordinate geometry. I've read Loney's book on coordinate geometry in which he says that to ... 2 votes 1 answer 41 views ### Problem With Transformation of Coordinates In S.L. Loney's book on Coordinate Geometry, he introduces the reader a way to switch from one origin of coordinates to another. The method he shows is: to change the origin to the point (h,k) you ... 4 votes 0 answers 56 views ### Removing four terms from the decic using a Tschirnhausen transformation? I. Transformation In this 2021 paper, one can remove four terms from an equation of degree n using a Tschirnhausen transformation of degree n-1 (and with radical coefficients), but only if n\... 2 votes 1 answer 87 views ### Generalization of Gauss multiplication formula for \Gamma(jm+kn+a);j,k\in\Bbb N? A hypergeometric single sum, like a Mittag Leffler function uses the Pochhammer symbol (a)_n multiplication formula to easily have a univariate hypergeometric function _p\text F_q closed form:\...
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I. Methods Using a quartic Tschirnhaus transformation, one can eliminate three terms $x^{n-1}, x^{n-2}, x^{n-3}$ without solving a $1\times2\times3 = 6$-deg equation, a simple explanation of which is ...