Jun 8, 2023 · An affine function between vector spaces is linear if and only if it fixes the origin. In the simplest case of scalar functions in one variable, linear functions are of the form f(x) = ax …

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 …

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?

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 point …

Aug 12, 2020 · On wikipedia I read that similarity transformation is a subgroup of affine transformation. But I didn't get the difference. Can someone explain it in easy words for …

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 …

Oct 22, 2020 · An open subset of an affine variety is a quasi-affine variety, and in 1.3 Hartshorne defines morphisms between varieties, which lets you write down a definition of a morphism …

仿射集 (Affine Set)和仿射包 (Affine hull)是凸优化中常见的两个概念。 仿射集 仿射包 仿射集 对于集合 C ⊆ R n C \subseteq R^ {n} ，如果通过集合 C C 中任意两个点的 直线 仍在集合 C C 中, …

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 …