Skrzyński, Marcin Irreducible algebraic sets of matrices with dominant restriction of the characteristic map. (English) Zbl 1016.15005 Math. Bohem. 128, No. 1, 91-101 (2003). Summary: We collect certain useful lemmas concerning the characteristic map, \(\mathcal {GL}_n\)-invariant sets of matrices, and the relative codimension. We provide a characterization of rank varieties in terms of the characteristic map as well as some necessary and some sufficient conditions for linear subspaces to allow the dominant restriction of the characteristic map. Cited in 1 Document MSC: 15A18 Eigenvalues, singular values, and eigenvectors 14A10 Varieties and morphisms Keywords:characteristic map; dominant map; linear subspace; \(\mathcal G\mathcal L_n\)-invariant set of matrices; rank variety PDFBibTeX XMLCite \textit{M. Skrzyński}, Math. Bohem. 128, No. 1, 91--101 (2003; Zbl 1016.15005) Full Text: EuDML