Kronecker modules and reductions of a pair of bilinear forms
Giovanni Falcone; M. Alessandra Vaccaro
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2004)
- Volume: 43, Issue: 1, page 55-60
- ISSN: 0231-9721
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topFalcone, Giovanni, and Vaccaro, M. Alessandra. "Kronecker modules and reductions of a pair of bilinear forms." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 43.1 (2004): 55-60. <http://eudml.org/doc/32359>.
@article{Falcone2004,
abstract = {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.},
author = {Falcone, Giovanni, Vaccaro, M. Alessandra},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {kronecker modules; bilinear forms; Kronecker module; bilinear form; reduction of pairs of bilinear forms},
language = {eng},
number = {1},
pages = {55-60},
publisher = {Palacký University Olomouc},
title = {Kronecker modules and reductions of a pair of bilinear forms},
url = {http://eudml.org/doc/32359},
volume = {43},
year = {2004},
}
TY - JOUR
AU - Falcone, Giovanni
AU - Vaccaro, M. Alessandra
TI - Kronecker modules and reductions of a pair of bilinear forms
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2004
PB - Palacký University Olomouc
VL - 43
IS - 1
SP - 55
EP - 60
AB - 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.
LA - eng
KW - kronecker modules; bilinear forms; Kronecker module; bilinear form; reduction of pairs of bilinear forms
UR - http://eudml.org/doc/32359
ER -
References
top- Dickson L. E., Equivalence of pairs of bilinear or quadratic forms under rational transformations, Trans. AMS 10 (1909), 347–360. (1909) MR1500845
- Dieudonné J., Sur la reduction canonique des couples de matrices, Bull. Soc. math. France 74 (1946), 130–146. (1946) Zbl0061.01307MR0022826
- Gabriel P., APPENDIX: Degenerate Bilinear Forms, J. Algebra 31 (1974), 67–72. (1974) Zbl0282.15014MR0347868
- Kronecker L., Algebraische Reduktion der Scharen bilinearer Formen, Sitzungsber. Akad. Berlin (1890), 763–776.
- Riehm C., The equivalence of bilinear forms, J. Algebra 31 (1974), 45–66. (1974) Zbl0283.15016MR0347867
- Scharlau R., Paare alternierender Formen, Math. Z. 147 (1976), 13–19. (1976) Zbl0304.15008MR0419484
- Waterhouse W., Pairs of quadratic forms, Inventiones Math. 37 (1976), 157–164. (1976) Zbl0337.10015MR0427230
- Waterhouse W., Pairs of symmetric bilinear forms in characteristic 2, Pacific J. Math. 69, 1 (1977), 275–283. (1977) MR0466015
- Williamson J., The equivalence of non-singular pencils of Hermitian matrices in an arbitrary field, Amer. J. Math. 57 (1935), 475–490. (1935) Zbl0012.00403MR1507088
- Williamson J., Note on the equivalence of nonsingular pencils of Hermitian matrices, Bull. AMS 51 (1945), 894–897. (1945) Zbl0060.03504MR0014046
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