# Tagged Questions

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), ...

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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 ...
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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. ...
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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?
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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 ...
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### Integral becomes improper after a substitution

I'm suprised about the following phenomenon which I would like to discuss with you. Consider the proper integral $$\int_{\pi/4}^{\pi/2}\frac{1}{\sin(x)}dx.$$ Since $\sin(x)$ is a diffeomorphism on ...
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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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### “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.
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