Is this a type-o or intentional?

  • Thread starter tolove
  • Start date
In summary, The conversation discusses the definition and use of the Levi-Civita symbol in mathematical notation and its relation to vector components. The symbol is defined as a permutation of 123 and is used in the cross-product of vectors. The conversation also clarifies the use of 'typo' as a short form for typographical error.
  • #1
tolove
164
1
I've been staring at this confused for a while now, and I've just realized that this might be a type-o. Should I assume that the Levi-Civita symbol is only defined on j,k, and that the i is a type-o, or is there an unwritten rule with this notation that gives the i a meaning?

[itex]\sum[/itex]j[itex]\sum[/itex]k εi,j,kj,k
 
Physics news on Phys.org
  • #2
Nominally that kind of sum would represent ith component of a vector. However, since δjk is zero if j≠k and εijk is zero if j=k, this is a complicated way of writing the zero vector.
 
  • #3
Minor pedantic point: The word is "typo", which is short for typographical error.
 
  • #4
D H said:
Nominally that kind of sum would represent ith component of a vector. However, since δjk is zero if j≠k and εijk is zero if j=k, this is a complicated way of writing the zero vector.

Thank you very much! The i isn't being defined because it doesn't matter what i is in this situation.

And to mark... I didn't know that, thanks
 
  • #5
tolove said:
I've been staring at this confused for a while now, and I've just realized that this might be a type-o. Should I assume that the Levi-Civita symbol is only defined on j,k, and that the i is a type-o, or is there an unwritten rule with this notation that gives the i a meaning?

[itex]\sum[/itex]j[itex]\sum[/itex]k εi,j,kj,k

No typo: the standard ε-symbol, used, eg., in writing vector cross-products in 3 dimensions, is:
[tex] \epsilon_{i j k} = \left\{ \begin{array}{rccl}
1 &\text{ if }& ijk &\text{ is an even permutation of 123}\\
-1&\text{ if }&ijk & \text{ is an odd permutation of 123}\\
0 &&&\text{ otherwise }
\end{array} \right. [/tex]

So, for example, the ith component of ##\vec{C} = \vec{A} \times \vec{B}## is ##C_i = \sum_{j,k} \epsilon_{ijk} A_j B_k##.

BTW: 'type-o' is a category of blood (for blood donations); what you probably mean is 'typo'.
 

FAQ: Is this a type-o or intentional?

1.

What is a type-o in scientific writing?

A type-o, also known as a typo, is a mistake or error in spelling, grammar, or punctuation in written scientific work. It can be unintentional or accidental, and can affect the accuracy and credibility of the research.

2.

How can I avoid making type-os in my scientific writing?

To avoid making type-os, it is important to carefully proofread and edit your work multiple times. It can also be helpful to have someone else read over your work to catch any errors that you may have missed. Using spelling and grammar checkers can also be beneficial.

3.

Is it acceptable to have type-os in my scientific writing?

No, it is not acceptable to have type-os in scientific writing as it can lead to misinterpretation of data and can decrease the credibility of the research. It is important to strive for accuracy and precision in all scientific writing.

4.

What are the consequences of having type-os in my scientific writing?

Having type-os in scientific writing can result in the rejection of your work by editors and reviewers, as well as negatively impact the perception of your research by other scientists in the field. It can also lead to confusion and errors in the interpretation of your findings.

5.

Should I correct type-os in published scientific papers?

If you discover type-os in your published scientific paper, it is recommended to contact the journal and request a correction. This ensures the accuracy and credibility of your work and helps prevent any misinterpretation by readers. It is important to strive for accuracy in all published scientific papers.

Back
Top