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We generalise the formula expressing the matrix trace of a given squarematrix as the integral of the numerical values of $A$ over the Euclidean sphereto the unit spheres of finite-dimensional normed spaces that have a 1-symmetricbasis. Our result is new even in the case of $\ell_p$-norms in $\mathbb{R}^N$for $p\neq 2$.

The trace as an average over the unit sphere of a normed space with a 1-symmetric basis