Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [kronecker-symbol]

For questions on kronecker symbols, a generalization of the Jacobi symbol to all integers.

In number theory, the Kronecker symbol, written as ${\displaystyle \left({\frac {a}{n}}\right)}$ or ${\displaystyle (a|n)}$, is a generalization of the Jacobi symbol to all integers.

58 questions
6
votes
1 answer

Confusion about the Kronecker $\delta$

Something disturbs me, concerning the Kronecker $\delta$. Assuming these hold: $$\delta_{ij}\delta_{jk}=\delta_{ik}$$ $$\delta_{ij}=\delta_{ji}$$ $$\delta_{ii}=1$$ does it follow that for every $\delta_{ij}$ we have…
Whyka
  • 1,953
3
votes
2 answers

Levi Civita and Kronecker Delta

I've been working on some quantum mechanics problems and arrived to this one where I have to deal with subscripts. I got stuck doing this: I have $\epsilon_{imk}\epsilon_{ikn}=\delta_{mk}\delta_{kn}-\delta_{mn}\delta_{kk}$. But then I went to check…
RicardoP
  • 215
1
vote
1 answer

Constructing an expression involving Kronecker delta and Levi-Civita symbol

Let $i,j,k,l\in\{0,1,2\}$. I am looking for a simple expression $f(i,j,k,l)$ involving only (Kronecker delta) $$\delta_{ab}=\cases{1&if $a=b$\\0&else},$$ and (Levi-Civita symbol) $$\epsilon_{ab} = \cases{1&if $ab$\\0&if $a=b$},$$ and…
Daniel Robert-Nicoud
  • 29,795
0
votes
2 answers

what is squared of a Kronecker ij?

Is it right to write $\delta_{ij}\delta_{ij}=(\delta_{ij})^2=\delta_{ij}$?
MathArt
  • 1,053
0
votes
1 answer

Compute $s_1 t_k \delta_{ii} \delta_{k1} \delta_{nn}$

I am in an argument with a friend from the university and we would like to clarify our problem: We have given the following term to calculate: $$s_1 t_k \delta_{ii} \delta_{k1} \delta_{nn}$$ All indices are running from 1 to 3 (3 dimensional…
Finn Eggers
  • 932
0
votes
0 answers

Levi Civita product proof

Does anyone know/know where to find the proof of: $$\epsilon_{ijk}\epsilon_{lmn} = +δ_{il}δ_{jm}δ_{kn} + δ_{im}δ_{jn}δ_{kl} + δ_{in}δ_{jl}δ_{km} −δ_{im}δ_{jl}δ_{kn} − δ_{il}δ_{jn}δ_{km} − δ_{in}δ_{jm}δ_{kl}$$ Thank you much
Garbojax McBruce
  • 1