By Eliezer Estrecho To prove this formula, we use the following: Where: and Using the equation above: We can factor out in the first term to give: Note that for the second term, the permutation of indices are odd, rearranging them to ijk will give the negative: Thus, About the author: Eliezer Estrecho is currently […]

Roel N. Baybayon MSPhysics1 ————————————————————————————————– We are going to prove the following vector identity using Levi-Civita symbol: Solution: Let    ,     ,   ,   . Then, By definition: We have to let m=n so that, Levi-Civita symbol can be expressed in terms of Kronecker delta given by: Thus,    

Author: Kayrol Ann B. Vacalares The divergence of a curl is always zero and we can prove this by using Levi-Civita symbol. The Levi-Civita symbol, also called the permutation symbol or alternating symbol, is a mathematical symbol used in particular in tensor calculus. Prove that: = 0 Proof: Let: and To show that:  = 0 First,       Here are the possible […]

Applying and in Proving the Vector Formula:  By: Quennie J. Paylaga   Prove: using Kronecker Delta Function and Levi-Civita Symbol.     To prove this, we let We can write the expression for in summation form as:      where where i, j, l are dummy summation variables. Each of which can be any letter […]

Author: CHRISTINE ADELLE L. RICO Here is another method of verifying a vector formula using the Levi-Civita symbol. Levi-Civita symbol is a tensor of rank three and is defined by +1 if the indices are in even permutation of , -1 if the indices are in odd permutation, and 0 if any two indices are […]