کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4603556 1336964 2008 21 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Quaternionic matrices: Unitary similarity, simultaneous triangularization and some trace identities
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Quaternionic matrices: Unitary similarity, simultaneous triangularization and some trace identities
چکیده انگلیسی

We construct six unitary trace invariants for 2×2 quaternionic matrices which separate the unitary similarity classes of such matrices, and show that this set is minimal. We have discovered a curious trace identity for two unit-speed one-parameter subgroups of Sp(1). A modification gives an infinite family of trace identities for quaternions as well as for 2×2 complex matrices. We were not able to locate these identities in the literature. We prove two quaternionic versions of a well known characterization of triangularizable subalgebras of matrix algebras over an algebraically closed field. Finally we consider the problem of describing the semi-algebraic set of pairs (X,Y) of quaternionic n×n matrices which are simultaneously triangularizable. Even the case n=2, which we analyze in more detail, remains unsolved.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 428, Issue 4, 1 February 2008, Pages 890-910