Difference between k-simplex and affine k-simplex

  • Thread starter ehrenfest
  • Start date
  • #1
ehrenfest
2,020
1

Homework Statement


http://en.wikipedia.org/wiki/Affine_simplex

Can someone please explain the difference between a k-simplex and an affine k-simplex? Is the difference just that in a k-simplex, the points do not have to be affinely independent? On the wikipedia page, they say in the introduction that the points need to be affinely independent even for a k-simplex.


Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
cristo
Staff Emeritus
Science Advisor
8,140
74
I was say, judging on that Wikipedia page, that a simplex and an affine simplex are the same thing. Of course, Wiki isn't entirely correct. Have you seen the terms used in different ways? Could you tell us where you have used the terms used?
 
  • #3
Vid
402
0
A regular simplex is one with vertices at the standard basis vectors. An affine simplex is an affine transformation (linear transform + a translation) of the standard simplex. Affine transformations preserve colinearity and ratios of line segments of the same line. An affine simplex is a k-simplex.
 
  • #4
ehrenfest
2,020
1
I was say, judging on that Wikipedia page, that a simplex and an affine simplex are the same thing.

OK good, that would resolve my confusion.

Of course, Wiki isn't entirely correct. Have you seen the terms used in different ways? Could you tell us where you have used the terms used?

No I haven't seen them used in different ways.
 

Suggested for: Difference between k-simplex and affine k-simplex

Replies
9
Views
492
Replies
6
Views
329
Replies
16
Views
733
Replies
2
Views
365
  • Last Post
Replies
2
Views
544
Replies
2
Views
455
Replies
7
Views
2K
Replies
4
Views
1K
Replies
2
Views
570
Top