= Odd dimension of a periodic Chebyshev system
A <Chebyshev system> of real <continuous functions> on a circle has odd dimension. If its dimension is $d$, take $d$ cyclically ordered evaluation points and move them continuously to the next cyclic permutation without letting points collide. The evaluation <determinant> stays nonzero, so cannot change sign. The final cyclic row permutation multiplies it by $(-1)^{d-1}$; consequently $d$ must be odd. For example, $1,\cos x,\sin x,\ldots,\cos mx,\sin mx$ has dimension $2m+1$ and the required zero bound.
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