| Title:
|
On the linear capacity of algebraic cones (English) |
| Author:
|
Skrzyński, Marcin |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
127 |
| Issue:
|
3 |
| Year:
|
2002 |
| Pages:
|
453-462 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
irreducible algebraic cone |
| Keyword:
|
linear subspace |
| Keyword:
|
conjugacy class of a matrix |
| Keyword:
|
quadratic form |
| MSC:
|
15A03 |
| MSC:
|
15A63 |
| MSC:
|
15A99 |
| idZBL:
|
Zbl 1007.15002 |
| idMR:
|
MR1931329 |
| DOI:
|
10.21136/MB.2002.134075 |
| . |
| Date available:
|
2009-09-24T22:03:37Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134075 |
| . |
| Reference:
|
[1] R. A. Brualdi, K. L. Chavey: Linear spaces of Toeplitz and nilpotent matrices.J. Comb. Theory, Ser. A 63 (1993), 65–78. MR 1213131, 10.1016/0097-3165(93)90025-4 |
| Reference:
|
[2] H. Flanders: On spaces of linear transformations of bounded rank.J. London Math. Soc. 37 (1962), 10–16. MR 0136618 |
| Reference:
|
[3] F. R. Gantmacher: Théorie des matrices.Dunod, Paris, 1966. Zbl 0136.00410 |
| Reference:
|
[4] M. Gerstenhaber: On dominance and varieties of commuting matrices.Ann. Math. 73 (1961), 324–348. Zbl 0168.28201, MR 0132079, 10.2307/1970336 |
| Reference:
|
[5] M. Gerstenhaber: On nilalgebras and linear varieties of nilpotent matrices, IV.Ann. Math. 75 (1962), 382–418. Zbl 0112.26403, MR 0171815 |
| Reference:
|
[6] S. Lang: Algebra.W. A. Benjamin, New York, 1970. Zbl 0216.06001 |
| Reference:
|
[7] B. Mathes, M. Omladič, H. Radjavi: Linear spaces of nilpotent matrices.Linear Algebra Appl. 149 (1991), 215–225. MR 1092879, 10.1016/0024-3795(91)90335-T |
| Reference:
|
[8] M. Omladič, P. Šemrl: Matrix spaces with bounded number of eigenvalues.Linear Algebra Appl. 249 (1996), 29–46. MR 1417407, 10.1016/0024-3795(95)00253-7 |
| Reference:
|
[9] R. Re: A note on linear subspaces of determinantal varieties.Le Matematiche 50 (1995), 173–178. Zbl 0861.14045, MR 1373578 |
| Reference:
|
[10] I. R. Shafarevich: Basic Algebraic Geometry.Springer, Berlin, 1977. Zbl 0362.14001, MR 0447223 |
| Reference:
|
[11] M. Skrzyński: Rank functions of matrices.Univ. Iagell. Acta Math. 37 (1999), 139–149. |
| Reference:
|
[12] M. Skrzyński: On ${\mathcal GL}_n$-invariant cones of matrices with small stable ranks.Demonstratio Math. 33 (2000), 243–254. MR 1769417 |
| . |
