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 …

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?

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 beginners of the topic?

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. ...

My naive understanding of this affine/not affine business is that for an affine variety we can write down something like a global coordinate system (the coordinate ring), while for a general algebraic variety …

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 that a s...

Jul 6, 2015 · Definition 1: Affine n n -space is kn k n without the origin. No; this is wrong. Affine n n -space is our geometric idea of what an arbitrary kn k n should look like. Say we are looking at a …