کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4603469 1336962 2008 8 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
A note on an unusual type of polar decomposition
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
A note on an unusual type of polar decomposition
چکیده انگلیسی

Motivated by applications in the theory of unitary congruence, we introduce the factorization of a square complex matrix A of the form A=SU, where S is complex symmetric and U is unitary. We call this factorization a symmetric–unitary polar decomposition or an SUPD. It is shown that an SUPD exists for every matrix A and is always nonunique. Even the symmetric factor S can be chosen in infinitely many ways. Nevertheless, we show that many properties of the conventional polar decomposition related to normal matrices have their counterparts for the SUPD, provided that normal matrices are replaced with conjugate–normal ones.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 429, Issue 1, 1 July 2008, Pages 42-49