Past exam of the mathematical methods I course of the University of Oxford / 2018 / 2 / b

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- Solution b

Solution

Choose the linear relation

c = M d, c_{i} = M_{ij} d_{j} .

Then the displayed tensor contraction is

(a_{i} c_{i}) b_{k} - (a_{i} b_{i}) c_{k} = (a \cdot c) b_{k} - (a \cdot b) c_{k}

, precisely the

k

th vector component of

a \times (b \times c)

by the vector triple product identity. The matrix

M

need not be a symmetric matrix.

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