Jun 8, 2023 · An affine function is the composition of a linear function with a translation, so while the linear part fixes the origin, the translation can map it somewhere else.

我整理一下我查到的资料： “仿射”这个词，翻译自英语affine，为什么会翻译出这两个字，我没查到。 英语affine，来自于英语affinity。英语词根fin来自于拉丁语finis，表示“边界，末端”，例如finish、final等 …

It may be more fruitful to compare groups of transformations. Speaking of groups acting on a Cartesian space, with the analogous questions in parentheses: orthogonal transformations ("What is an inner …

Jun 10, 2015 · A line has been chosen at infinity, and the affine transformations are those projective transformations fixing this line. Therefore, abstractly, the use of the extra parameters is to describe …

Dec 25, 2012 · Affine geometry is like projective geometry with one line (the “distinguished line”) labeled “remove this to obtain an affine plane”. In this sense, an affine space is a projective space with …

Recently, I am struglling with the difference between linear transformation and affine transformation. Are they the same ? I found an interesting question on the difference between the functions. ...

First, do you understand the definition of affine space that the authors have given? If so, can you distinguish between the notion of a vector space and the notion of an affine space?

Oct 17, 2022 · Regarding your first question: The Zariski topology on any closed subvariety is induced from the ambient space, so for example a quasi-affine variety can be obtained by removing a closed …

May 2, 2017 · Roughly speaking, affine independence is like linear independence but without the restriction that the subset of lower dimension the points lie in contains the origin. So three points in …

Jul 9, 2012 · Of course, this is (essentially) the point of the proof that cohomology vanishes for affine schemes though--so nothing really new here. :) Thanks again for the nice answer!