# Questions tagged [kronecker-symbol]

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

42 questions
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### what is squared of a Kronecker ij?

Is it right to write $\delta_{ij}\delta_{ij}=(\delta_{ij})^2=\delta_{ij}$?
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### How to show that the isotropic tensor of order n is a multiple of the kronecker delta

I have already found this question here but with the property of invariant under rotation. However I don't have this property and I want to prove that $T_{ij} = \alpha \delta _{ij}$ where $T_{ij}$ ...
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### Turning this double sum with Kronecker delta into a single sum - am I correct?

I would be grateful if you checked my solution: $$\sum^{\lfloor j/2 \rfloor}_{q=0} \sum^{\lfloor k/2\rfloor}_{s=0} \frac{2^{k-2s}A^{q+s}}{q!s!(k-2s)!}\delta_{j-2q,k-2s}$$ Here $\lfloor \rfloor$ ...
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### Clarify the definition of a transition matrix

I am reading the book Matrix Variate Distribution by A. K. Gupta and D. K. Nagar. In the first chapter (Definition 1.2.8), they define a matrix $B_{p}$ ($p \in \mathbb{N}^{\ast}$) as follows : ...
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### Show $\int v^2 \left( v_i v_j - \frac13 v^2 \delta_{ij} \right) f_m d^3v = 0 ,$

I need to show, that $$\int v^2 \left( v_i v_j - v^2 \delta_{ij} \right) f_m d^3v = 0 ,$$ where $$f_m \propto \exp(-v^2),$$ is Maxwellian distributin. Actually, those indicies frustrates me, I know ...
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### Kronecker Zeta function

If we define the Kronecker symbol K(a,n) as at Wikipedia, can we define $$\zeta_K(s,a) = \sum_n \dfrac{K(a,n)}{n^s}$$? If so, what does it equal?