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 …

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 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 …

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 …

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?

Apr 14, 2017 · 10 Note that the second definition is a generalisation of the first. A set is affine iff it contains all lines through any two points in the set (hence, as a trivial case, a set containing a single …

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. ...

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 using an …

According to this definition the subset $\ { (0,0); (0,1)\}$ is an affine subspace, while this is not so according to the usual definition of an affine subspace.