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
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Tridiagonal forms in low dimensions
چکیده انگلیسی
Pati showed that every 4 × 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 U = 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
نویسندگان
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