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[MUSIC] In this lecture I want to introduce two mathematical objects that are widely used in applied mathematics. The reason that we need that at this point is because Im going to use them to derive vector identities in the next lecture. So the first one is the Kronecker delta, so whats the definition of the Kronecker delta? It has a symbol delta thats a small delta and it has two indices i and j. Were talking about 3 dimensional space, so i and j can take the value of one, two or three. So for instance delta 1,1 or delta 1,2 or delta 1,3 or delta 2,1 etc. And then this has two distinct values, it will be equal to 1, in the case when i is equal to j so delta 1,1 is 1 delta 2,2 is 1 and delta 3,3 is 1. And its equal to 0 if i is not equal to j, so something like delta 1,2 or delta 1,3 would be 0. Thats the Kronecker Delta, the other symbol is the Levi Civita symbol, thats an epsilon. This is an epsilon that has three indices i, j and k of course you dont