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 …

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 …

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.

It appears you are working with Affine Transformation Matrices, which is also the case in the other answer you referenced, which is standard for working with 2D computer graphics.

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 …

Jun 6, 2021 · This follows from the relationship of unions/intersections of ideals and algebraic sets. When we have an affine algebraic set or an affine variety, we want to look at what the …

Note that M is a composite matrix built from fundamental geometric affine transformations only. Show the initial transformation sequence of M, invert it, and write down the final inverted …

Jun 24, 2017 · What is the difference between linearly and affinely independent vectors? Why does affine independence not imply linear independence necessarily? Can someone explain …

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?

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 …