 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-2-of-the-natural-sciences-course-of-the-university-of-cambridge/2013/paper-2/6/i/solution

For a constant orthogonal Cartesian coordinate change

x_{i}^{'} = Q_{ij} x_{j}

u_{i}^{'} = Q_{ij} u_{j}, B_{ij}^{'} = Q_{i p} Q_{j q} B_{pq}, Q^{T} Q = I .

Repeated indices are summed. Each index of an ordinary Cartesian tensor contributes one factor of

Q

. A pseudotensor would have an additional determinant factor under an orientation-reversing transformation; the rules here concern ordinary tensors.

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