# 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).

160 questions
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### extracting rotation, scale values from 2d transformation matrix

How can I extract rotation and scale values from a 2D transformation matrix? ...
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### Causal Inverse Z-Transform of Fibonacci

Say the Fibonacci sequence is defined by: $y(n) = y(n-1) + y(n-2)$ initial conditions: $y(0)=0, y(1)=1$ I incorporate those initial conditions as: $y(n) = y(n-1) + y(n-2) + \delta(n-1)$ I ...
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### Solving a cubic polynomial equation.

Overview I have tried finding a solution to this problem myself and I have flailed. Its just a challenge for me. could you please tell me how far am I in solving this question? My approach for ...
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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 ...
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### How do I find the matrix with respect to a different basis?

I tried to solve this question but the answer is totally different, can you explain how to solve it
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### On the Fourier transform of $f(x)=\ln(x^2+a^2)$

I would like to derive the Fourier transform of $f(x)=\ln(x^2+a^2)$, where $a\in \mathbb{R}^+$ by making use of the properties: \mathcal{F}[f'(x)]=(ik)\hat{f}(k)\\ \mathcal{F}[-ixf(x)...
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### A linear transform of a closed set is closed

A linear transform of a closed set $E\subset \mathbb{R}^d \to \mathbb{R}^d$ is closed. I have seen a lot of similar questions here, but none of them exactly addresses the issue. Please if you find it ...
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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 ...
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### How do I map the torus to a plane?

Please see my answer on Perlin noise first. A bit of background. Imagine a solid texture, like an actual block of sky and cloud. If you "cut a sheet" of sky and display it as an image, you'd get ...
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### Find and sketch the image of the straight line $z = (1+ia)t+ib$ under the map $w=e^{z}$

I need to find and sketch the image of the straight line $z = (1+ia)t +aib$, where $-\infty < t < + \infty$, $a,b\in \mathbb{R}$, and $a \neq 0$, under the map $w = e^{z}$. In order to ...
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### Why do we define a linear transformation to have the property that $f(cW)=c f(W)$?

Why we define a lin tranfs to have the property that $f(cW)=c f(W)$ ? let $V,T$ be any two vector spaces and let $f:V\rightarrow T$ be a linear transformation between $V$and $T$ why do we ...
I'm trying to construct a homeomorphism from $[0,1]\times[0,1]$ to $\overline{D}(0,1)$. I'm pretty sure there is one. I've been trying to work geometrically : mapping $[0,1]\times[0,1]$ to $[-1/2,1/2]... 1answer 66 views ### Biliniear form to inner product Let$f:V\times V\rightarrow F$be a bilinear form in a finite inner product space V. If$F=R$, how can I prove that there exists a single linear transformation$T:V \rightarrow V$so that for each$v,...
I am given that $V$ is n-dimensional vector space over $\mathbb{C}$ and $T \in L(V)$. And $T$ has least $m$ distinct nonzero eigenvalues. How do I show that \$\text{null}(T^{n-m}) = \text{null}(T^{n-m+...