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).

# Questions tagged [transformation]

2744 questions

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### Fourier Transform of a Polynomial

Suppose you are given the polynomial
\begin{equation}
f(x)=1+x^3
\end{equation}
and the definition of Fourier transform:
\begin{equation}
\hat{f}(k)=\frac{1}{\sqrt{2\pi}}\int_{-\infty}^{\infty}e^{-ikx}f(x)dx, k\in…

Bazinga

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### How do I convert the distance between two lat/long points into feet/meters?

I've been reading around the net and everything I find is really confusing. I just need a formula that will get me 95% there. I have a tool that outputs the distance between two lat/long points.
Point 1: 32.773178, -79.920094
Point 2:…

Micah

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### Finding a Rotation Transformation from two Coordinate Frames in 3-Space

The question I'm trying to figure out states that I have 3 points P1, P2 and P3 in space. In one frame (Frame A I called it) those points are: Pa1, Pa2 and Pa3, same story for Frame B (namely: Pb1, Pb2 and Pb3).
Whats the rotation matrix from one…

challengerTA

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### Get Transformation Matrix from Points

I have built a little C# application that allows visualization of perpective transformations with a matrix, in 2D XYW space. Now I would like to be able to calculate the matrix from the four corners of the transformed square. Here is a screenshot to…

Kendall Frey

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### Matrix for rotation around a vector

I'm trying to figure out the general form for the matrix (let's say in $\mathbb R^3$ for simplicity) of a rotation of $\theta$ around an arbitrary vector $v$ passing through the origin (look towards the origin and rotate counterclockwise). This is…

chris

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### How to figure of the Laplace transform for $\log x$?

I was looking at a table of common Laplace transforms of functions when I came across the transform for $\log x$. Apparently, the transform is as follows:
$$\mathcal{L} \left\{ \log x\right\}=-\frac{1}{s}\left(\log s + \gamma\right)$$
where…

Argon

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### How to transform gaussian(normal) distribution to uniform distribution?

I have gaussian distributed numbers with mean 0 and variance 0.2.
And I want to transform this distribution to uniform distribution [-3 3].
How can I transform gaussian distribution numbers to uniform distribution?

Hyungchan Song

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### Why is the momentum a covector?

Can someone tell me why the momentum is an element of the cotangent space?
More detailed: if we have some smooth manifold M and the cotangent space $T_{x}M^{*}$ I know that the momentum p is an element of $T_{x}M^{*}$, but I have no intuition why.…

user247741

**14**

votes

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### Finding a matrix representation of the transpose transformation

Define $T : M_{n×n}(\mathbb{R}) → M_{n×n}(\mathbb{R})$ by $T(A) := A^t$.
I know this transformation is linear and just takes a matrix and spits out it's transpose. I also know that the transpose is just a matrix with it's columns and rows swapped;…

David South

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### What kind of transformation an upper triangular matrix represents

Every matrix represents a linear transformation, but depending on characteristics of the matrix, the linear transformation it represents can be limited to a specific type. For example, an orthogonal matrix represents a rotation (and possibly a…

Alireza Mirian

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### Using quaternions instead of 4x4 matrices for transformations

I'm interested in implementing a clean solution providing an alternative to 4x4 matrices for 3D transformation. Quaternions provide the equivalent of rotation, but no translation. Therefore, in addition to a Quaternion, you need an additional vector…

Dov

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### When is it allowed to do operations like 'differentiating both sides', 'integrating both sides'?

In books, I often come across situations when they differentiate both sides of an equation or integrate both sides, apply Laplace transform on both sides, etc. Like it's as simple as multiplying both sides or dividing both sides by some constant.
Is…

Ryder Rude

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### A limit and a coordinate trigonometric transformation of the interior points of a square into the interior points of a triangle

The coordinate transformation (due to Beukers, Calabi and Kolk)
$$x=\frac{\sin u}{\cos v}$$
$$y=\frac{\sin v}{\cos u}$$
transforms the square domain $0\lt x\lt 1$ and $0\lt y\lt 1$ into the triangle domain $u,v>0,u+v<\pi /2$ (in Proofs from the BOOK…

Américo Tavares

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### Graphing $f(2-x)$

Sorry for this very trivial question, but I've become slightly confused by this question. Consider a graph
$y=f(x)$. How would I draw the graph $y=f(2-x)$?
It seems to me that as this is obviously equal to $y=f(-(x-2))$ this should represent the…

A-Level Student

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### Jacobian of Fourier Transformation

I am trying to calculate the Jacobian determinate of the Fourier transform which I stumbled upon when studying the Path Integral in Quantum Field Theory. I know the answer should be $1$ but I don't know how to show it. The transform…

JeffDror

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