# 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).

155 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 ...
How can i calculate the Fourier transform of a delayed cosine? I haven't found anywhere how to do that. This is my attempt in hoping for a way to find it without using the definition: x(t) = cos(... 1answer 6k views ### How to find the orthonormal transformation that will rotate a vector to the x axis? I am having trouble remembering linear algebra. I need to find the orthonormal transformation that will rotate a 3-dimensional vector to the x axis. I could not find any similar question on the net. ... 4answers 5k views ### 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 ... 2answers 1k views ### Prove two commutative linear transformations on a vector space over an algebraically closed field can be simultaneously triangularized Prove two commutative linear transformations on a finite-dimensional vector space V over an algebraically closed field can be simultaneously triangularized. It is equivalent to show if AB=BA, ... 1answer 5k views ### Find linear transformation given kernel Find linear transformation F in canonical bases given  F: \Bbb R^4 \to \Bbb R^3   \ker F=\operatorname{span}\left\{\begin{bmatrix}1\\2\\3\\4\end{bmatrix}, \begin{bmatrix}0\\1\\1\\1\end{bmatrix} ... 5answers 2k views ### Transformation T is… “onto”? I thought you have to say a mapping is onto something... like, you don't say, "the book is on the top of"... Our book starts out by saying "a mapping is said to be onto R^m", but thereafter, it just ... 2answers 326 views ### suppose |a|<1, show that \frac{z-a}{1-\overline{a}z} is a mobius transformation that sends B(0,1) to itself. Suppose |a|<1, show that f(x) = \frac{z-a}{1-\overline{a}z} is a mobius transformation that sends B(0,1) to itself. To make such a mobius transformation i tried to send 3 points on the edge ... 1answer 4k views ### Transformation of ellipsoid to sphere So I need to find an volume-preserving mapping from an ellipsoid to a ball (solid sphere). (Specifically: \dfrac{x^2}9 + y^2 + z^2 \le 3, but I'd rather understand the general case than just get ... 0answers 333 views ### Algorithm to determine matrix equivalence I'm a physicist who's not particularly good at linear algebra so please accept my apologies if this is standard textbook stuff that I'm just unaware of. I have two real rectangular matrices A_{mxn} ... 1answer 2k views ### How to find the rotation matrix that will align an arbitrary vector to an axis If I have a vector that starts at the origin, how can I find the transformation matrix that will align it with the positive y-axis. So it basically turns into a positive-y axis? EDIT: I also forgot ... 1answer 600 views ### Elliptic Coordinates - Inverting the transformation The standard way to transform elliptic coordinates (\mu, \nu) \ to Cartesian coordinates (x,y): x = a \cosh(\mu) \cos(\nu) y = a \sinh(\mu) \sin(\nu) Is there any way to get the ... 2answers 2k views ### 3d transformation two triangles I have two triangles in 3d. I need to calculate transformation matrix(3X3) between two triangles in 3D. 1)How can I calculate the transformation matrix(rigid) while fixing one of the points to the ... 0answers 194 views ### Proof for a summation-procedure using the matrix of Eulerian numbers? I've discussed a procedure for divergent summation using the matrix of Eulerian numbers occasionally in the last years (initially here, and here in MSE and MO but not in that generality and thus(?) ... 2answers 168 views ### 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 ... 1answer 158 views ### Homeomorphism from [0,1]\times[0,1] to \overline{D}(0,1)? 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]... 4answers 189 views ### 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 ... 2answers 4k views ### 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 ... 1answer 346 views ### Linear Transformations finding matrix in respect to a basis and coordinate change matrix. Define T: Poly_2 \ to\ Poly_2 byT(at^2+bt+c)=3ct^2 +2at-b$$1) Show that T is a linear transformation and give a matrix A for T with respect to the basis B=\{t^2,t,1\}. 2) Give a ... 2answers 39 views ### Triple integration, Spherical coordinates How do we get limit such as 0\le\theta\le\pi, 0\le\phi\le2\pi in spherical coordinate system where$$x=r \sin\theta\cos\phi, y=r \sin\theta\sin\phi, z=r \cos\theta Why is the $\theta$-limit $[0,... 1answer 64 views ### Biliniear form to inner product Let$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+...