Differential of the coordinate functions

  • #1
3
0
Hello folks,
I'm glad that I discovered this forum. :) You might save me.
I'm hearing right now differential geometry and am having some problems with the subject.
May you explain me the follwoing. We had the special case of the i-th projection. My lecturer now posited that the differential of the i-th projection is again the i-th projection. Can you explain me how to see that?

Greetings
Rico
 

Answers and Replies

  • #2
13,457
10,516
Without any further context, it's simply the following: The differential of a linear map is again the linear map.
##\varphi\, : \,x\longmapsto a\cdot x## gets ##\dfrac{d}{dx}\varphi(x) = a## which is ##D\varphi = L_a\, : \,x \longmapsto L_a(x)=a\cdot x##.
 

Related Threads on Differential of the coordinate functions

Replies
5
Views
2K
  • Last Post
Replies
3
Views
2K
Replies
2
Views
2K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
7
Views
1K
Replies
4
Views
2K
Replies
0
Views
2K
  • Last Post
Replies
1
Views
2K
Replies
18
Views
3K
Replies
8
Views
3K
Top