Irreducible algebraic sets of matrices with dominant restriction of the characteristic map

Marcin Skrzyński

Mathematica Bohemica (2003)

  • Volume: 128, Issue: 1, page 91-101
  • ISSN: 0862-7959

Abstract

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We collect certain useful lemmas concerning the characteristic map, 𝒢 L 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.

How to cite

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Skrzyński, Marcin. "Irreducible algebraic sets of matrices with dominant restriction of the characteristic map." Mathematica Bohemica 128.1 (2003): 91-101. <http://eudml.org/doc/249219>.

@article{Skrzyński2003,
abstract = {We collect certain useful lemmas concerning the characteristic map, $\{\mathcal \{G\}L\}_n$-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.},
author = {Skrzyński, Marcin},
journal = {Mathematica Bohemica},
keywords = {characteristic map; dominant map; linear subspace; $\mathcal \{G\}\mathcal \{L\}_n$-invariant set of matrices; rank variety; characteristic map; dominant map; linear subspace; -invariant set of matrices; rank variety},
language = {eng},
number = {1},
pages = {91-101},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Irreducible algebraic sets of matrices with dominant restriction of the characteristic map},
url = {http://eudml.org/doc/249219},
volume = {128},
year = {2003},
}

TY - JOUR
AU - Skrzyński, Marcin
TI - Irreducible algebraic sets of matrices with dominant restriction of the characteristic map
JO - Mathematica Bohemica
PY - 2003
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 128
IS - 1
SP - 91
EP - 101
AB - We collect certain useful lemmas concerning the characteristic map, ${\mathcal {G}L}_n$-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.
LA - eng
KW - characteristic map; dominant map; linear subspace; $\mathcal {G}\mathcal {L}_n$-invariant set of matrices; rank variety; characteristic map; dominant map; linear subspace; -invariant set of matrices; rank variety
UR - http://eudml.org/doc/249219
ER -

References

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  1. Rank varieties of matrices, Commutative Algebra (Berkeley, CA). Math. Sci. Res. Inst. Publ. 15, Springer, New York, 1989, pp. 173–212. (1989) MR1015518
  2. Théorie des matrices, Dunod, Paris, 1966. (1966) Zbl0136.00410
  3. 10.1090/S0002-9947-97-01975-2, Trans. Amer. Math. Soc. 349 (1997), 3401–3408. (1997) MR1432201DOI10.1090/S0002-9947-97-01975-2
  4. Algebra, W. A. Benjamin, Inc., New York, 1970. (1970) Zbl0216.06001
  5. Introduction to Complex Analytic Geometry, Birkhäuser, Basel, 1991. (1991) MR1131081
  6. Basic Algebraic Geometry, Springer, Berlin, 1977. (1977) Zbl0362.14001MR0447223
  7. Remarks on applications of rank functions to algebraic sets of matrices, Demonstratio Math. 32 (1999), 263–271. (1999) MR1710249
  8. On 𝒢 L n -invariant cones of matrices with small stable ranks, Demonstratio Math. 33 (2000), 243–254. (2000) MR1769417
  9. On 𝒢 L n -invariant algebraic cones of matrices with relative codimension equal to 1 , Commentationes Math. 40 (2000), 167–174. (2000) MR1810393
  10. 10.1007/BF01388851, Invent. Math. 98 (1989), 229–245. (1989) Zbl0717.20033MR1016262DOI10.1007/BF01388851

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