# Questions tagged [kronecker-symbol]

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

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### How do I simplify $\delta_{ij} \delta^{jk}$?

How do I simplify $\delta_{ij} \delta^{jk}$? I know that $\delta_{ij} \delta_{jk}=\delta_{ik}$, but what do I do if the there's a Kronecker Delta symbol with upper indices and one with lower indices?
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### Prove that $\delta_{jl}\delta_{im}=\delta_{jm}\delta_{il}$

Prove that $\delta_{jl}\delta_{im}=\delta_{jm}\delta_{il}$ In the video, he directly cancelled $$3\delta_{jl}\delta_{im}-3\delta_{jl}\delta_{im}$$ and similar terms. I was thinking if subscript ...
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### Difficult vector identity using Levi Civita

I have to prove the following: $$[3(\vec{p}\cdot\hat{r})\hat{r}-\vec{p}]\times[3(\vec{m}\cdot\hat{r})\hat{r})-\vec{m}]=-2\vec{p}\times\vec{m}+3\hat{r}[\hat{r}\cdot(\vec{p}\times\vec{m})]$$ I am given ...
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### Reducing tensor of rank two into Kronecker delta

I want to understand how this particular equality is true, and here we need to use the idea of contraction of tensors to achieve this theorem? $a_{ij}$ x $a^{ij} = \delta_j^j$ Here, a is a tensor of ...
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### How to multiply a vector and a square matrix with Kronecker product, and know the answer's shape? [closed]

$\mathbf{1}_n \in \mathbb{I}^{n\times 1}$ is a vector of ones with shape $n\times 1$ $\mathbf{I}_m \in \mathbb{I}^{m\times m}$ is an identity matrix with shape $m\times m$ What is the answer to, and ...
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### Can I write $\frac {\partial E_{rs}} {\partial E_{mn}} = \delta_{rsmn}?$

Can I write $\frac {\partial E_{rs}} {\partial E_{mn}} = \delta_{rsmn}?$ and then use that delta to change variables in another tensor like: $$C_{ijkl}\delta_{rskl} = C_{ijrs}$$ or is there ...
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### Show that the $n \times n$ identity matrix is commutative with any $n \times n$ martix using Suffix Notation

Using Suffix Notation, I have to show that the $n \times n$ identity matrix is commutative with any $n \times n$ martix with respect to matrix multiplication. We have just been introduced to the ...
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### 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 ...
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### Analytic floor function, why this seems to work?

I have been using this formula which I determined for myself for quite some time now for use in everything from the sgn() function to the Kronecker delta to the ceiling and NINT() functions but haven'...
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### Is there an opposite of the Kronecker Delta?

Instead of $\delta(n,n) = 1$ and $\delta (n,k) = 0$, is there something that returns $0$ when the arguments are the same, and $1$ when the arguments are different. Is there a special function that ...
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### Dipole-Coupling Tensor: Electrostatic Dipole Moments

I've been struggling with this problem today. Here's an image of the question I'm attempting to answer. I'm relatively new to tensor algebra (I've been studying it for about a week or two), and I've ...
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### Show that $δ_{KL}$ is a Cartesian tensor

By using the deﬁnition of the Kronecker delta $δ_{KL}$, show that $δ_{KL}$ is a Cartesian tensor, that is $δ'_{MN} = L_{MK}L_{NL}δ_{KL}$ under the rotation $X_K = L_{MK}X'_M$. Solution: Using the ...
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### Kronecker delta equation simplification

I am trying to simplify a tensor equation with Kronecker delta $$A_{ij} \big ( \delta_{ik}\delta_{jm} -\frac{1}{3}\delta_{ij}\delta_{km} \big)$$ $A$ and $\delta$ are Cartesian tensors. I know ...
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### Why is the delta function the continuous generalization of the kronecker delta and not the identity function?

In a discrete $n$ dimensional vector space the Kronecker delta $\delta_{ij}$ is basically the $n \times n$ identity matrix. When generalizing from a discrete $n$ dimensional vector space to an ...
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### A Summation Convention – Substitution Rule

I'm new to this forum. I'm starting a PhD – it's going to be a big long journey through the jungle that is CFD. I would like to arm myself with some tools before entering. The machete is Cartesian ...
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