Article
Keywords:
kronecker modules; bilinear forms
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.
References:
[1] Dickson L. E.:
Equivalence of pairs of bilinear or quadratic forms under rational transformations. Trans. AMS 10 (1909), 347–360.
MR 1500845
[2] Dieudonné J.:
Sur la reduction canonique des couples de matrices. Bull. Soc. math. France 74 (1946), 130–146.
MR 0022826 |
Zbl 0061.01307
[4] Kronecker L.: Algebraische Reduktion der Scharen bilinearer Formen. Sitzungsber. Akad. Berlin (1890), 763–776.
[8] Waterhouse W.:
Pairs of symmetric bilinear forms in characteristic 2. Pacific J. Math. 69, 1 (1977), 275–283.
MR 0466015
[9] Williamson J.:
The equivalence of non-singular pencils of Hermitian matrices in an arbitrary field. Amer. J. Math. 57 (1935), 475–490.
MR 1507088 |
Zbl 0012.00403
[10] Williamson J.:
Note on the equivalence of nonsingular pencils of Hermitian matrices. Bull. AMS 51 (1945), 894–897.
MR 0014046 |
Zbl 0060.03504