Multiplicative maps on invertible matrices that preserve matricial properties

@article{Guralnick2003MultiplicativeMO,
  title={Multiplicative maps on invertible matrices that preserve matricial properties},
  author={Robert M. Guralnick and Chi-Kwong Li and Leiba Rodman},
  journal={Electronic Journal of Linear Algebra},
  year={2003},
  volume={10},
  pages={24}
}
Descriptions are given of multiplicative maps on complex and real matrices that leave invariant a certain function, property, or set of matrices: norms, spectrum, spectral radius, elementary symmetric functions of eigenvalues, certain functions of singular values, (p, q )n umerical ranges and radii, sets of unitary, normal, or Hermitian matrices, as well as sets of Hermitian matrices with fixed inertia. The treatment of all these cases is unified, and is based on general group theoretic results… 

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