Evaluating Sum from j=1 to n: i=k

[whatisreality]

Homework Statement

Evaluate

∑$_{j=1}^{n} \delta_{ij} \delta_{jk}$ where 1≤i≤n and 1≤k≤n and

$\delta_{ij}$ and $\delta_{jk}$ = 1 if i=j

0 otherwise

Homework Equations

The Attempt at a Solution

I'm pretty unsure how to do this. I assume k and i are constant. If that's the case, wouldn't this sum always be zero unless k and i are equal? And 1 if they are equal? So does that mean there are two answers, depending on something that hasn't been specified (i.e. whether i and k are equal)?

 

[Samy_A]

If that's the case, wouldn't this sum always be zero unless k and i are equal? And 1 if they are equal?

That is the correct answer. You can write is as $\delta_{ik}$

 

[whatisreality]

That is the correct answer. You can write is as $\delta_{ik}$

Brilliant, thank you!