 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2004/paper-1/7/a/solution

The trace is unchanged by transposition and is cyclic under a product. With

S^{T} = S

and

A^{T} = - A

tr (A S) = tr [(A S)^{T}] = tr (- S A) = - tr (A S) .

Thus

tr (A S) = 0

. In components this is the vanishing contraction of a symmetric tensor with an antisymmetric tensor.

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