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 …

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 …

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?

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 …

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 …

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 …

Jul 6, 2015 · An affine space is a slightly restricted version of this where you only allow operations where $\sum r_i = 1$ ("affine linear combinations"). In particular you can't multiply by zero, so …

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 …

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 …

In reading about convex optimization, the author states that all convex sets are affine. Are affineness and convexity equivalent? If I understand, both definitions incorporate the notion …