# Tagged Questions

for questions about algebraic geometry that focus on affine space. For affine mappings in linear algebra (i.e. linear mappings plus translations), please use the linear-algebra tag or another appropriate tag.

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### Showing space closed under affine combinations is translation of vector space

I'm struggling to reconcile two different definitions of an affine space. The definition in my course notes is: An affine space in $\mathbb{R}^n$ is a non-empty subset closed under affine ...
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### why should add one column using Moore-Penrose pseudoinverse

I have a code from someone that I dont understand: This code is written in matlab and the function is to estimate linear geometric transformation [1] of a matrix using pinv. The size of first matrix ...
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Assuming I have given affine transformation $\mathbb{R}^3\to \mathbb{R}^3$ which has matrix representation $$\left[\begin{array}{cccc} 3&2&-3&-10\\ 4&10&-12&-29\\ ... 1answer 66 views ### Vector bundles on \mathbb{A}^1_k with doubled origin? One of the most common examples of gluing affine lines is the affine line \mathbb{A}^1_k with doubled origin. Out of curiousity, is there a known classfication of the vector bundles on this space? 2answers 52 views ### Affine transformation that sends a conic to itself but does not preserve the focci or the axes [closed] So I'm trying to find an affine transformation that sends a conic to itself but does not preserve the foci or the axes. I don't know if this can be done. I'm pretty sure that if it is possible then I ... 0answers 87 views ### When does a homogeneous morphism have only finite fibers? Suppose that we have a map {\bf f}:=(f_1,f_2,\cdots ,f_n):\mathbb{C}^n\rightarrow \mathbb{C}^n given by$$ \mathbb{C}^n\ni {\bf z}:=(z_1,z_1,\cdots,z_n)\rightarrow \big(f_1({\bf z}),f_2({\bf ...
For an affine variety $X$ with coordinate ring $A$ it is not hard to see that for $g\in A$ the basic open set (or distinguished open set) $$D(g):=\{ P\in X | g(P)\neq 0\}$$ is dense in $X$ if and only ...