# 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), (rigid-...

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### Distribution of $R^2 = X^2 +Y^2$ where (X,Y) is a point on the unit circle

So I have a point $(X,Y)$ chosen from the unit disk with uniform distribution. And I'm attempting to find the distribution of $R^2$, where $R$ is the distance from the point to the origin. Now ...
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### Can a linear transformation $\mathbb{R}^n \rightarrow \mathbb{R}^n$ have a complex eigenvector? [closed]

Can a transformation $\mathbb{R}^n \rightarrow \mathbb{R}^n$ have a complex eigenvector? Similarly, can a transformation $\mathbb{C}^n \rightarrow \mathbb{C}^n$ have a real eigenvector?
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### Defining a region in $\mathbb{R}^2$

I was trying to do this exercise but my answer doesn't match with the solution and I'm wondering why: Consider the coordinates transformation defined by $x=2u+v$ and $y=u^2-v$. Being $T$ the ...
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### Transformations of points in the plane

Hopefully somebody understands what I mean here, If take a polynomial with complex numbers as input, then I will get a complex number as an output. If the input and output are plotted on an Argand ...
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### Transformation of a real number 4 by 4 matrix to a 3 by 3 matrix

Are there any transformation methods that could be used to represent a $4\times 4$ matrix of real constants as a finite product/sum of $3\times 3$ (numeric: real or complex) matrices?
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### True or false: Every transformation T: Cn --> Cn (n ≥ 2) has n distinct eigenvectors

True or false: 1) Every transformation T: Cn --> Cn (n ≥ 2) has n distinct eigenvectors 2) Every transformation T: Cn --> Cn (n ≥ 2) has at least 1 eigenvector 3) Every transformation T: Rn --> Rn (...
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### Polar Coordinate Conversion (Integration)

I want to convert some integrals to use polar coordinates as my differentials, my problem is getting the limits. So this is the first concept I am not understanding: If I have a circle in the xy-...