Nilpotent Matrices

  • Thread starter brydustin
  • Start date
  • #1
205
0

Main Question or Discussion Point

I am curious how to derive the (I+N)^-1 = I - N + N^2 - N^3 + .... N^(k-1) + 0
Where N^k = O, because we assume that N is nilpotent.

Actually I'm just supposed to show that the inverse always exists (for my homework), but I'm not asking how to find existence, I want to know how this equation is derived (assuming existence).

Thanks.....
 

Answers and Replies

  • #2
22,097
3,280
What happens if you multiply

[tex](I+N)(I-N+N^2-N^3+...N^{k-1})[/tex]
 
  • #3
205
0
AH! Thanks.... all the "middle parts fall out

I - N + N - N^2 + N ^2 -...... - N^(k-1) +N^(k+1) + N^k

and you are left with Identity, which shows that its the inverse. Thanks :)
 

Related Threads on Nilpotent Matrices

  • Last Post
Replies
9
Views
4K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
3
Views
4K
  • Last Post
Replies
7
Views
3K
Replies
2
Views
2K
Replies
7
Views
7K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
1
Views
2K
Top