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.

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 …

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 …

An Affine space abstracts the affine combinations. You can think of an affine combination as a weighted average, or a convex hull (if you limit the coefficients to be between 0 and 1).

Jun 1, 2017 · Thus, the affine cone over a projective variety is a cone whose ''horizontal slices'' recover the variety you started with. Notice that the cone is always singular at the origin. By …

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 …

Sep 11, 2021 · According to this definition of affine spans from wikipedia, "In mathematics, the affine hull or affine span of a set S in Euclidean space Rn is the smallest affine set …

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 …

Apr 23, 2022 · An affine transformation is composed of rotations, translations, scaling and shearing. In 2D, such a transformation can be represented using an augmented matrix by $$ …