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 …

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 …

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?

Ok, thank you, Fly. The affine transform in 3D is just application of 3D rotation matrix+shift vector to the initial (x,y,z) and then x_projection, y_projection = arctan (x/z), arctan (y/z). Thank you. I'm now trying …

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...

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. ...

It appears you are working with Affine Transformation Matrices, which is also the case in the other answer you referenced, which is standard for working with 2D computer graphics.

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.

I am trying to understand the concept of affinity of functions. First, I thought that every affine function has to be a linear function, too, because my teacher's notes define linear and affine fun...