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MATHEMATICA BOHEMICA, Vol. 128, No. 1, pp. 91-101 (2003)
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Irreducible algebraic sets of matrices with dominant restriction of the characteristic map

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Marcin Skrzynski

* Marcin Skrzynski*, Institute of Mathematics, Cracow University of Technology, ul. Warszawska 24, PL 31-155 Krakow, e-mail: ` pfskrzyn@cyf-kr.edu.pl`

**Abstract:** We collect certain useful lemmas concerning the characteristic map, ${\cal GL}_n$-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.

**Keywords:** characteristic map, dominant map, linear subspace, $\Cal G\Cal L_n$-invariant set of matrices, rank variety

**Classification (MSC2000):** 15A18, 14A10

**Full text of the article:**

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