I am a bit confused. What is the difference between a linear and affine function? Any suggestions will be appreciated.
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 product space?"), linear transformations ("What is a vector space?"), affine transformations ("What is an affine space?").
intuition - What is the affine space and what is it for? - Mathematics ...
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. ...
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?
Affine geometry is like projective geometry with one line (the “distinguished line”) labeled “remove this to obtain an affine plane”. In this sense, an affine space is a projective space with additional information.
The whole point of the representation you're using for affine transformations is that you're viewing it as a subset of projective space. 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 where the line at infinity moves during the projective transformation.
I am reading this introduction to Mechanics and the definition it gives (just after Proposition 1.1.2) for an affine subspace puzzles me. I cite: A subset $B$ of a ...