# 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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### Kronecker delta from cardinal sine

One possible definition for Dirac's delta function is via a limit of the cardinal sine, according to \begin{equation} \lim_{a\rightarrow 0}\int_{-\infty}^\infty \frac{1}{a} \mathrm{sinc}\left(\frac{x}...
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### A question on deriving a kronecker delta identity

I've recently come across the following identity: $$\frac{1}{\sqrt{n!m!}}\bigg(\frac{\mathrm{d}}{\mathrm{d}Z^{\ast}}\bigg)^{m}\big(Z^{\ast}\big)^{n}\bigg\vert_{Z^{\ast}\to 0}=\delta_{n,m}\;.$$ Here is ...
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### Kronecker delta for inequality

Kronecker delta return 1, or 0 depending on a conditional statement (if $i = j$), for example, $\delta_{i,j} = 1$ if $i = j$, and $\delta_{i,j} = 0$ otherwise. I would like to know if there are ...
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### Relation between the differential operator, a vector and the Kronecker delta

I saw in a textbook, $D_{c}x_{i} = \delta_{ci}$. Could someone explain this to me?
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### Understanding of the Kronecker delta

From my understanding $e_a\cdotp e_b$ = $\delta_{ab}$ (for $a,b = 1,2,3$) equals $1$ when $a=b$ and $0$ when $a \neq b$ where $e_a$ and $e_b$ are vectors with entries 1 in the $a$'th and $b$'th row, ...
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### Levi-Civita and Kronecker delta notation

I was wondering how to do the following $\epsilon_{ijk}\sigma_{jk}=\epsilon_{iji}=0$ I get this is $0$ but don't understand how they got the $\epsilon_{iji}$
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### what does it mean to be symmetric for tensors and Kronecker delta symbols and help explain this answer to me

i understand how to change 2 tensors into Kronecker delta symbols but unsure how they managed to transform back to just one. If someone could add all the steps to get to the answer that would be ...
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### Evaluating $\int_{-1}^{1} x P_{n}(x) P_{m}(x) dx$

I was trying to evaluate - $\int_{-1}^{1} x P_{n}(x) P_{m}(x) dx$ Point is there is a $x$ in the integrand, otherwise, it is a well known integral which results to $\frac{2}{2n+1}$ if $m=n$ and $0$ ...
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### How to proof that a dual basis applied to the basis give the Kronecker delta?

Since a long time I was wondering how can we build proof that a basis applies to its dual give the Kronecker delta. I'm now following on-line lectures related to topology and find out that there is a ...
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### Looking for ${f_n}$ such that $\int_0^1 (x-t)^{m-1}f_n(t) dt = \delta_{n,m}$

Good day, I am wondering whether it is possible to find a sequence of functions $f_n$ such that $$\int_0^1 (1-t)^{m-1}f_n(t) dt = \delta_{n,m}$$ for every $0<n,m$. Thank you.
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### Definition of Elementary Matrices

I'm a bit confused about the definition of elementary matrices which are used to represent elementary row operations on an extended coefficient matrix when doing the Gaussian elimination. In my ...
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### Proof of $(\mu*1)=\delta_1$ where $(f*g)$ is Dirichlet Convolution

I was interested in the proof for this fact because it is used to prove M$\ddot o$bius Inversion Formula. However, I did not completely understand how proof wiki used a series of binomial coefficients ...
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### Einstein Summation Notation and Kronecker Delta Problem

Evaluate $\delta_j^iv_iu^j, \delta^2_j\delta^j_kv^k,$ and $\delta^3_j\delta^j_1$. The Kronecker-delta: https://en.wikipedia.org/wiki/Kronecker_delta Einstein notation: https://en.wikipedia.org/wiki/...