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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### 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…

kjo

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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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votes

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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…

Learn_and_Share

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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 $g(z)=e^{i\varphi}f(e^{i\theta}z)$,…

lzk

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