Please me to understand Einstein notation and permutations

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SUMMARY

This discussion focuses on understanding Einstein notation and permutations, specifically the expression A_ij = e_ijk a_k. The user seeks clarity on how to represent this equation as a matrix, acknowledging the role of the Kronecker delta and the Levi-Civita symbol. Key resources provided include links to the Wikipedia page on the Levi-Civita symbol and MathWorld's explanation of the permutation symbol. The user assumes familiarity with the summation convention, which is essential for grasping the concepts discussed.

PREREQUISITES
  • Understanding of Einstein summation convention
  • Familiarity with matrix notation (A_ij)
  • Knowledge of the Levi-Civita symbol (e_ijk)
  • Basic concepts of permutations in mathematics
NEXT STEPS
  • Study the properties and applications of the Levi-Civita symbol
  • Learn about the Kronecker delta and its role in tensor operations
  • Explore matrix representations of tensor equations
  • Review permutation groups and their significance in linear algebra
USEFUL FOR

Students and professionals in mathematics, physics, and engineering who are looking to deepen their understanding of tensor calculus and its applications in various fields.

Tiggy
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Hey,
Can anyone help me to understand einstein notation and permutations? I have a book, but it's not very clear. I really don't understand how you can write A_ij = e_ijk a_k out as a matrix? To start with I understand that a matrix can be represented as A_ij where i is the row and j is the column. However, I don't understand as soon as k and the kronecker delta become involved! Anyone know of any good way to explain this or books or websites??

Thank you!
 
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