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 Incoming links: Trace orthogonality of symmetric and antisymmetric matrices

Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2003 / Paper 2 / 8 / b / ii / Solution Created 2026-10-18 Updated 2026-10-20

Apply trace orthogonality of symmetric and antisymmetric matrices. In detail, invariance of the trace under transpose and its cyclic property give

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

Therefore

tr (S A) = 0

. The negative sign comes from

A^{T} = - A

, while

S^{T} = S

.

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