1. Math
  2. Algebra
  3. l sometimes it is useful to introduce special matrices to...

Question: l sometimes it is useful to introduce special matrices to...

Question details

l. Sometimes it is useful to introduce special matrices to facilitate calculations and derivations. Let i, j, k є {1.23}. In class, we defined the Kronecker delta as I if i j We can also define a completely antisymmetric symbol, called a Levi-Civita symbol, as -1 0 if(i, j. k) = (3,2, l), (2, 1.3), ( 1.3, 2) if any two of the indices are the same Eijk It is clear that Ejk-jik, Ejk -j and eijk-Ekj that is, exchanging any two indices of the Levi-Civita symbol changes the sign. It is easiest to just remember that even permutations of (1,2,3) give a value of 1 and odd permutations give a value of-1. Let a = (al, a2,a3) and b = (bi, b2. b3). (a) Compute the quantity c given by (b) Do you recognize this result? Can you rewrite c in terms of a and b in a more familiar form2

Solution by an expert tutor
Blurred Solution
This question has been solved
Subscribe to see this solution