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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Laplace, Legendre, Fourier, Hankel, Mellin, Hilbert, Borel, Z...: unified treatment of transforms?

I understand "transform methods" as recipes, but beyond this they are a big mystery to me. There are two aspects of them I find bewildering. One is the sheer number of them. Is there a unified framework that includes all these transforms as…
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"Well defined" function - What does it mean?

What does it mean for a function to be well-defined? I encountered with this term in an excersice asking to check if a linear transformation is well-defined.
AndrePoole
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What do I use to find the image and kernel of a given matrix?

I had a couple of questions about a matrix problem. What I'm given is: Consider a linear transformation $T: \mathbb R^5 \to \mathbb R^4$ defined by $T( \vec{x} )=A\vec{x}$, where $$A = \left(\begin{array}{crc} 1 & 2 & 2 & -5 & 6\\ -1 & -2 &…
StealzHelium
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Is a Fourier transform a change of basis, or is it a linear transformation?

I've frequently heard that a Fourier transform is "just a change of basis". However, I'm not sure whether that's correct, in terms of the terminology of "change of basis" versus "transformation" in linear algebra. Is a Fourier transform of a…
user541686
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Can non-linear transformations be represented as Transformation Matrices?

I just came back from an intense linear algebra lecture which showed that linear transformations could be represented by transformation matrices; with more generalization, it was later shown that affine transformations (linear + translation) could…
Justin L.
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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? matrix = [1, 0, 0, 1, 0, 0] matrix.rotate(45 / 180 * PI) matrix.scale(3, 4) matrix.translate(50, 100) matrix.rotate(30 / 180 * PI) matrix.scale(-2, 4) Now my matrix have…
Tolgahan Albayrak
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Is hyperbolic rotation really a rotation?

We define a $2\times 2$ Givens rotation matrix as: $${\bf G}(\theta) = \begin{bmatrix} \cos(\theta) & -\sin(\theta) \\ \sin(\theta) &\cos(\theta) \end{bmatrix}.$$ On the other hand, we define a $2\times 2$ hyperbolic rotation matrix as: $${\bf…
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Is it true that any matrix can be decomposed into product of rotation,reflection,shear,scaling and projection matrices?

It seems to me that any linear transformation in $R^{n\times m}$ is just a series of applications of rotation(actually i think any rotation can be achieved by applying two reflections, but not sure), reflection, shear, scaling and projection…
Sunny88
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Shift numbers into a different range

I was wondering how can I shift my data that fall between a range lets say [0, 125] to another range like [-128, 128]. Thanks for any help
ealiaj
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Will every rational number eventually be in this set?

Let $A_0=\{0\}$. For every $n\ge 0$, let $B_n=\bigcup_{k\ge 0}A_n+k$, and let $A_{n+1}=f(B_n)$, where $f:[0,\infty)\to[0,1):x\mapsto\frac{x}{x+1}$. Let $q\in\Bbb Q\cap [0,1)$. Can we prove that $q\in A_n$ for some $n\ge 0$? Equivalently, I would…
G Tony Jacobs
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Going from a value inside $[-1,1]$ to a value in another range

How does one calculate the value within range $-1.0$ to $1.0$ to be a number within the range of e.g. $0$ to $200$, or $0$ to $100$ etc. ?
some_id
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Show that $\phi: \mathbb{R}_3[x]\rightarrow\mathbb{R}^3, \phi(p):=[p(-1), p(0), p(1)] $ is a linear transformation

Let $\mathbb{R}_3[x]$ be a vector space of polynomials p with degree $\leq3$ and show that $\phi: \mathbb{R}_3[x]\rightarrow\mathbb{R}^3, \phi(p):=[p(-1), p(0), p(1)] $ is a linear transformation. Now I know that transformation is linear if these…
Mathfan
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How to transform a set of 3D vectors into a 2D plane, from a view point of another 3D vector?

I googled around a bit, but usually I found overly-technical explanations, or other, more specific Stackoverflow questions on how 3D computer graphics work. I'm sure I can find enough resources for this eventually, but I figured that it's good…
jcora
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How does multiplying by trigonometric functions in a matrix transform the matrix?

I found this comic: But I can't understand the humor because I can't understand how trig functions affect matrix multiplication. Can someone please explain?
Joe
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Is an entire function "determined by" its maximum modulus on each circle centered at the origin?

Let $f$ be an entire function, and $$M_f(r)=\max_{|z|\leq r}|f(z)|$$ denotes its maximum modulus on the circle centered at the origin with radius $r>0$. It's clear that for any entire functions $f(z)$ and $g(z)=e^{i\varphi}f(e^{i\theta}z)$,…
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