# Marcell Gaal: Isometries of matrices

Source: Algebra and functional analysis seminar

**Abstract**:

This talk is concerned with isometries on certain substructures of matrices.

First, we compute the group of isometries on traceless Hermitian matrices with respect to any unitary similarity invariant norm.

Second, we point out that our proof techniques could be applied to verify an existing result, which is due to Li and Tsing (1991), concerning isometries on skew-symmetric matrices with respect to any orthogonal congruence invariant norm.

Furthermore, we apply the latter structural result to determine certain generalized isometries of the special orthogonal group. This extends a former result of Hatori, Abe and Akiyama (2013) on c-spectral isometries of the special orthogonal group.

Finally, I will also mention some open problems.

Joint work with Robert Guralnick.

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Vljudno vabljeni!

Roman Drnovšek in Primož Moravec