| Title:
|
Kronecker modules and reductions of a pair of bilinear forms (English) |
| Author:
|
Falcone, Giovanni |
| Author:
|
Vaccaro, M. Alessandra |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
43 |
| Issue:
|
1 |
| Year:
|
2004 |
| Pages:
|
55-60 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We give a short overview on the subject of canonical reduction of a pair of bilinear forms, each being symmetric or alternating, making use of the classification of pairs of linear mappings between vector spaces given by J. Dieudonné. (English) |
| Keyword:
|
kronecker modules |
| Keyword:
|
bilinear forms |
| MSC:
|
11E04 |
| MSC:
|
11E39 |
| MSC:
|
13C05 |
| MSC:
|
15A04 |
| MSC:
|
15A63 |
| idZBL:
|
Zbl 1069.11013 |
| idMR:
|
MR2124602 |
| . |
| Date available:
|
2009-08-21T12:54:03Z |
| Last updated:
|
2012-05-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/132949 |
| . |
| Reference:
|
[1] Dickson L. E.: Equivalence of pairs of bilinear or quadratic forms under rational transformations.Trans. AMS 10 (1909), 347–360. MR 1500845 |
| Reference:
|
[2] Dieudonné J.: Sur la reduction canonique des couples de matrices.Bull. Soc. math. France 74 (1946), 130–146. Zbl 0061.01307, MR 0022826 |
| Reference:
|
[3] Gabriel P.: APPENDIX: Degenerate Bilinear Forms.J. Algebra 31 (1974), 67–72. Zbl 0282.15014, MR 0347868 |
| Reference:
|
[4] Kronecker L.: Algebraische Reduktion der Scharen bilinearer Formen.Sitzungsber. Akad. Berlin (1890), 763–776. |
| Reference:
|
[5] Riehm C.: The equivalence of bilinear forms.J. Algebra 31 (1974), 45–66. Zbl 0283.15016, MR 0347867 |
| Reference:
|
[6] Scharlau R.: Paare alternierender Formen.Math. Z. 147 (1976), 13–19. Zbl 0304.15008, MR 0419484 |
| Reference:
|
[7] Waterhouse W.: Pairs of quadratic forms.Inventiones Math. 37 (1976), 157–164. Zbl 0337.10015, MR 0427230 |
| Reference:
|
[8] Waterhouse W.: Pairs of symmetric bilinear forms in characteristic 2.Pacific J. Math. 69, 1 (1977), 275–283. MR 0466015 |
| Reference:
|
[9] Williamson J.: The equivalence of non-singular pencils of Hermitian matrices in an arbitrary field.Amer. J. Math. 57 (1935), 475–490. Zbl 0012.00403, MR 1507088 |
| Reference:
|
[10] Williamson J.: Note on the equivalence of nonsingular pencils of Hermitian matrices.Bull. AMS 51 (1945), 894–897. Zbl 0060.03504, MR 0014046 |
| . |
