# Questions tagged [vector-spaces]

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### are angles betwen a basis and a given vector correlated? [closed]

I was thinking about an orthogonal basis and some vector, and maybe, find some relation between the angles that form the basis with the given vector
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### What are the eigenvalues and eigenvectors of a composition of two arbitrary linear transformations? [closed]

Let $S$ and $T$ be two linear transformations on $\mathbb{R}^n$. We can find the eigenvalues and eigenvectors of $S$ and $T$. I am trying to find out the relation(s) among the eigenvalues and ...
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### How to calculate the camera 3D position if I know 4 points in the picture of the camera [closed]

I've got a picture of - let's say a - table and I measured 4 Points on this table. I define my table as "ground level", so my Points got the coordinates (px, py, 0). Is it possible to calculate the ...
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### Spectral theory without topology

How much of spectral theory can be developed just working with vector spaces (finite or infinite dimensional) without referring to a choice of topology ? Something along these lines, for example: ...
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### Axiom(s) of choice and bases of vector spaces

I'm not sure this question is more suitable for MO or for MSE, so feel free to move it to MSE if necessary. I work here in ZF theory. Consider the following statements: $(C)$ Axiom of choice: for ...
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### Growth in a vector space

I am interested in "growth" in finite vector spaces. I have been wondering about the veracity of the following statement: Statement: For every $\varepsilon>0$ there exists $b\in\mathbb{Z}^+$ ...