کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
9498263 | 1631194 | 2005 | 20 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Tridiagonal forms in low dimensions
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله

چکیده انگلیسی
Pati showed that every 4Â ÃÂ 4 matrix is unitarily similar to a tridiagonal matrix. We give a simple proof. In addition, we show that (in an appropriate sense) there are generically precisely 12 ways to do this. When the real part is diagonal, it is shown that the unitary can be chosen with the form UÂ =Â PD where D is diagonal and P is real orthogonal. However even if both real and imaginary parts are real symmetric, there may be no real orthogonal matrices which tridiagonalize it. On the other hand, if the matrix belongs to the Lie algebra sp4(C), then it can be tridiagonalized by a unitary in the symplectic group Sp(2). In dimension 5 or greater, there are always rank three matrices which are not tridiagonalizable.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 407, 15 September 2005, Pages 169-188
Journal: Linear Algebra and its Applications - Volume 407, 15 September 2005, Pages 169-188
نویسندگان
Kenneth R. Davidson, Dragomir Ž. ÄokoviÄ,