On the linear capacity of algebraic cones

Marcin Skrzyński

Mathematica Bohemica (2002)

  • Volume: 127, Issue: 3, page 453-462
  • ISSN: 0862-7959

Abstract

top
We define the linear capacity of an algebraic cone, give basic properties of the notion and new formulations of certain known results of the Matrix Theory. We derive in an explicit way the formula for the linear capacity of an irreducible component of the zero cone of a quadratic form over an algebraically closed field. We also give a formula for the linear capacity of the cone over the conjugacy class of a “generic” non-nilpotent matrix.

How to cite

top

Skrzyński, Marcin. "On the linear capacity of algebraic cones." Mathematica Bohemica 127.3 (2002): 453-462. <http://eudml.org/doc/249059>.

@article{Skrzyński2002,
abstract = {We define the linear capacity of an algebraic cone, give basic properties of the notion and new formulations of certain known results of the Matrix Theory. We derive in an explicit way the formula for the linear capacity of an irreducible component of the zero cone of a quadratic form over an algebraically closed field. We also give a formula for the linear capacity of the cone over the conjugacy class of a “generic” non-nilpotent matrix.},
author = {Skrzyński, Marcin},
journal = {Mathematica Bohemica},
keywords = {irreducible algebraic cone; linear subspace; conjugacy class of a matrix; quadratic form; irreducible algebraic cone; linear subspace; conjugacy class of matrices; quadratic form; linear capacity},
language = {eng},
number = {3},
pages = {453-462},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the linear capacity of algebraic cones},
url = {http://eudml.org/doc/249059},
volume = {127},
year = {2002},
}

TY - JOUR
AU - Skrzyński, Marcin
TI - On the linear capacity of algebraic cones
JO - Mathematica Bohemica
PY - 2002
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 127
IS - 3
SP - 453
EP - 462
AB - We define the linear capacity of an algebraic cone, give basic properties of the notion and new formulations of certain known results of the Matrix Theory. We derive in an explicit way the formula for the linear capacity of an irreducible component of the zero cone of a quadratic form over an algebraically closed field. We also give a formula for the linear capacity of the cone over the conjugacy class of a “generic” non-nilpotent matrix.
LA - eng
KW - irreducible algebraic cone; linear subspace; conjugacy class of a matrix; quadratic form; irreducible algebraic cone; linear subspace; conjugacy class of matrices; quadratic form; linear capacity
UR - http://eudml.org/doc/249059
ER -

References

top
  1. 10.1016/0097-3165(93)90025-4, J. Comb. Theory, Ser. A 63 (1993), 65–78. (1993) MR1213131DOI10.1016/0097-3165(93)90025-4
  2. On spaces of linear transformations of bounded rank, J. London Math. Soc. 37 (1962), 10–16. (1962) MR0136618
  3. Théorie des matrices, Dunod, Paris, 1966. (1966) Zbl0136.00410
  4. 10.2307/1970336, Ann. Math. 73 (1961), 324–348. (1961) Zbl0168.28201MR0132079DOI10.2307/1970336
  5. On nilalgebras and linear varieties of nilpotent matrices, IV, Ann. Math. 75 (1962), 382–418. (1962) Zbl0112.26403MR0171815
  6. Algebra, W. A. Benjamin, New York, 1970. (1970) Zbl0216.06001
  7. 10.1016/0024-3795(91)90335-T, Linear Algebra Appl. 149 (1991), 215–225. (1991) MR1092879DOI10.1016/0024-3795(91)90335-T
  8. 10.1016/0024-3795(95)00253-7, Linear Algebra Appl. 249 (1996), 29–46. (1996) MR1417407DOI10.1016/0024-3795(95)00253-7
  9. A note on linear subspaces of determinantal varieties, Le Matematiche 50 (1995), 173–178. (1995) Zbl0861.14045MR1373578
  10. Basic Algebraic Geometry, Springer, Berlin, 1977. (1977) Zbl0362.14001MR0447223
  11. Rank functions of matrices, Univ. Iagell. Acta Math. 37 (1999), 139–149. (1999) 
  12. On 𝒢 L n -invariant cones of matrices with small stable ranks, Demonstratio Math. 33 (2000), 243–254. (2000) MR1769417

NotesEmbed ?

top

You must be logged in to post comments.