# Questions tagged [kronecker-delta]

For questions about the Kronecker-delta, which is a function of two variables (usually non-negative integers).

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### Understanding Kronecker delta symbol & summation in 3D integral

I'm currently trying to practice finding the inertia tensor for simple rigid bodies, with the inertia tensor elements given by: $$I_{ij}=\int_{V}^{}\rho(\delta_{ij}\sum_{k}^{}x_{k}^2-x_{i}x_{j})dv$$ I ...
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### Kronecker delta expressed as a derivative when there are multiple indices.

For instance, when differentiating four-vectors the result is straightforward: $$\frac{\partial x^\mu}{\partial x^\nu}=\delta_\nu^\mu$$ as the derivative is only non-zero when the Lorentz indices ...
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### How is this probability distribution evaluated with Kronecker Delta and summation?

I am reading through Robert Swendsen's An Introduction to Statistical Mechanics and Thermodynamics, and in section 3.4, he provided an example of the probability of the sum of two dice using Kronecker ...
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### Can I exchange the indices in this particular product of Kronecker delta's?

Is the following true? (We are not using Einstein summation notation here) $$\delta_{mk} \delta_{nk} = \delta_{mn} \delta_{km}$$
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### Integrals of complex exponentials in terms of Kronecker deltas

Suppose that I have a set of of $L$ real parameters $\{\phi_1,\phi_2,\dots,\phi_L\}$, each of them taking values in the interval $[0,2\pi]$. I was wondering if there is a closed form for the following ...
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### how to factor out a term in Tensor notation

I am studying classical mechanics and I was asked in my homework to calculate poisson brackets of components of angular momentum. I couldn't understand how to approach, then I looked at the solution. ...
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### Summation in closed form

I have the following summation: $$f(k_1,k_2) = \sum_{l_1 = 0}^{k_1}\sum_{l_2 = 0}^{k_2} {\rho}^{l_1+l_2}\delta[k_1-k_2+l_2-l_1]$$ where $\rho$ is a constant and $\delta$ is ...
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