On orthogonal similarity classes of symmetric matrices and orthogonal $*$-conjugacy classes of Hermitian matrices
Tadej Starčič · arXiv (Cornell University) · 2020
We describe the recursive algorithmic procedure to compute the orbits and its dimensions of symmetric matrices with respect to the action of orthogonal similarity. Similarly, we provide the recursive algorithmic procedure to obtain the lower bounds for dimensions of orbits of Hermitian matrices with respect to the action of orthogonal $*$-conjugation. We also give the answer to the question concerning uniqueness of the normal forms of Hermitian matrices under orthogonal $*$-conjugation. It is applied to deduce the result on the uniqeness of a normal form of the quadratic part of a flat complex point.