intuition - What is the affine space and what is it for? - Mathematics . . . 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?")
affine geometry - What does it mean to be affinely independent, and . . . 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 space are affinely independent if the smallest flat thing containing them is a plane They're affinely dependent if they lie on a line (or are the same point) A set of points is affinely dependent if and only
What are differences between affine space and vector space? An Affine space abstracts the affine combinations You can think of an affine combination as a weighted average, or a convex hull (if you limit the coefficients to be between 0 and 1)
What is an Affine Span? - Mathematics Stack Exchange According to this definition of affine spans from wikipedia, quot;In mathematics, the affine hull or affine span of a set S in Euclidean space Rn is the smallest affine set containing S, or equiva
difference between similarity and affine transformation 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?