Double summation

  • #1
190
0

Main Question or Discussion Point

If I know that [itex]\sum_{k=1}^n a_{ik} = 1[/itex] and [itex]\sum_{j=1}^n b_{kj} = 1[/itex], why is the following permitted?

[tex]\sum_{j=1}^n \sum_{k=1}^n a_{ik}b_{kj} = \left(\sum_{j=1}^n b_{kj}\right) \left(\sum_{k=1}^n a_{ik}\right) = 1\cdot 1 = 1[/tex]


Thanks!
 

Answers and Replies

  • #2
22,097
3,277
It's not permitted. What you wrote makes no sense since you sum over k and one of the [itex]b_{kj}[/itex] is outside that sum. That is not allowed.

What you could do is:

[tex]\sum_{j=1}^n\sum_{k=1}^n a_{ik}b{kj}= \sum_{k=1}^n \sum_{j=1}^n a_{ik}b_{kj} = \sum_{k=1}^n \left(a_{ik} \sum_{j=1}^n b_{kj}\right)= \sum_{k=1}^n a_{ik}=1[/tex]
 
  • #3
190
0
Thank you very much. I knew I wasn't understanding something.
 

Related Threads for: Double summation

  • Last Post
Replies
3
Views
724
  • Last Post
Replies
3
Views
4K
  • Last Post
Replies
6
Views
3K
  • Last Post
Replies
7
Views
3K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
1
Views
3K
  • Last Post
Replies
5
Views
4K
  • Last Post
Replies
6
Views
1K
Top