کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5772926 | 1631058 | 2018 | 20 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Symplectic spaces and pairs of symmetric and nonsingular skew-symmetric matrices under congruence
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
Let F be a field of characteristic not 2, and let (A,B) be a pair of nÃn matrices over F, in which A is symmetric and B is skew-symmetric. A canonical form of (A,B) with respect to congruence transformations (STAS,STBS) was given by Sergeichuk (1988) [25] up to classification of symmetric and Hermitian forms over finite extensions of F. We obtain a simpler canonical form of (A,B) if B is nonsingular. Such a pair (A,B) defines a quadratic form on a symplectic space, that is, on a vector space with scalar product given by a nonsingular skew-symmetric form. As an application, we obtain known canonical matrices of quadratic forms and Hamiltonian operators on real and complex symplectic spaces.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 537, 15 January 2018, Pages 84-99
Journal: Linear Algebra and its Applications - Volume 537, 15 January 2018, Pages 84-99
نویسندگان
Victor A. Bovdi, Roger A. Horn, Mohamed A. Salim, Vladimir V. Sergeichuk,