# Questions tagged [affine-geometry]

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.

760 questions
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### Decomposition of 4x4 or larger affine transformation matrix to individual variables per degree of freedom

There are a couple of problems and solutions where affine matrices are decomposed into their separate transformations. However, they are all for the 2D case and I`m finding it difficult to generalise ...
3answers
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### Is there any incompatibility between affine spaces and Hilbert spaces? [closed]

I was wondering if there is such a thing like a Hilbertian affine space. I've seen the definition of an Euclidian affine space, which is: An affine space (A, V, φ) is an Euclidean affine space if ...
2answers
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### Prove that General Affine Transformations preserve ratios of lengths

Let $A$ be a matrix with determinant 1. Then we call a general affine transformation, a transformation of the form \begin{align*} \begin{bmatrix}x'\\y'\end{bmatrix}=A\begin{bmatrix}x\\y\end{bmatrix}+\...
1answer
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### prove that hyperbolic cone is affine set (check my solution)

Hyperbolic cone $C_P$ with $P$ positive definite matrix is a set that satisfies the following $C_P = \{x: x^TPx\leq (c^Tx)^2\}$. I need to prove that this set is affine. I know that this set is convex,...
1answer
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### Affine space and convex sets in the context of Euclidean space

I am a bit confused as to the relationship between the ideas of vector space, affine space, and convex sets in the context of Euclidean space $\mathbb{R}^d$. As of now, this is how I see it. \$\mathbb{...