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arXiv · 1709.04507

On isometry groups of self-adjoint traceless and skew-symmetric matrices

Marcell Gaál·Robert M. Guralnick
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Abstract

This note is concerned with isometries on the spaces of self-adjoint traceless matrices. We compute the group of isometries with respect to any unitary similarity invariant norm. This completes and extends the result of Nagy on Schatten $p$-norm isometries. Furthermore, we point out that our proof techniques could be applied to obtain an old result concerning isometries on skew-symmetric matrices.

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Marcell Gaál, Robert M. Guralnick. 2017-09-13. On isometry groups of self-adjoint traceless and skew-symmetric matrices. https://arxiv.org/abs/1709.04507

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