Exercise 1.7 The Kronecker completely antisymmetric symbol Eijk is defined by Eijk 1 if ijk is an even permutation of 12

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Exercise 1 7 The Kronecker Completely Antisymmetric Symbol Eijk Is Defined By Eijk 1 If Ijk Is An Even Permutation Of 12 1 (55.76 KiB) Viewed 48 times

Exercise 1.7 The Kronecker completely antisymmetric symbol Eijk is defined by Eijk 1 if ijk is an even permutation of 123 -1 if ijk is an odd permutation of 123 0 otherwise (1.105) The starting value is €123 = 1. A useful determinant form is Eijk = (1.106) Indices are here raised and lowered with the euclidean metric. A Verify the following statements: 1. the component k of the vector product of v and u is (ū x ū)% = eh ij v*W 2. in euclidean 3-dimensional space, an antisymmetric matrix with entries Mij is equivalent to a vector vk = } ekij Mij 3. the inverse formula is Mi; 1 / Eijk vk. B Calculate 1. Eijkeimn 33 2. Eijkeijn 3. Eijkelijk