Geodesic
Irreducible algebraic sets of matrices with dominant restriction of the characteristic map
Mathematica Bohemica, Tome 128 (2003) no. 1, pp. 91-101.

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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.
DOI : 10.21136/MB.2003.133938
Classification : 13A50, 14A10, 14L30, 15A03, 15A18
Keywords: characteristic map; dominant map; linear subspace; $\mathcal G\mathcal L_n$-invariant set of matrices; rank variety 
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Skrzyński, Marcin. Irreducible algebraic sets of matrices with dominant restriction of the characteristic map. Mathematica Bohemica, Tome 128 (2003) no. 1, pp. 91-101. doi : 10.21136/MB.2003.133938. http://geodesic.mathdoc.fr/articles/10.21136/MB.2003.133938/

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