کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5773236 | 1631079 | 2017 | 23 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
A new polar decomposition in a scalar product space
ترجمه فارسی عنوان
یک تجزیه قطبی جدید در یک فضای محصول اسکالر
دانلود مقاله + سفارش ترجمه
دانلود مقاله ISI انگلیسی
رایگان برای ایرانیان
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
چکیده انگلیسی
There are various definitions of right and left polar decompositions of an mÃn matrix FâKmÃn (where K=C or R) with respect to bilinear or sesquilinear products defined by nonsingular matrices MâKmÃm and NâKnÃn. The existence and uniqueness of such decompositions under various assumptions on F, M, and N have been studied. Here we introduce a new form of right and left polar decompositions, F=WS and F=Sâ²Wâ², respectively, where the matrix W has orthonormal columns (Wâ² has orthonormal rows) with respect to suitably defined scalar products which are functions of M, N, and F, and the matrix S is selfadjoint with respect to the same suitably defined scalar products and has eigenvalues only in the open right half-plane. We show that our right and left decompositions exist and are unique for any nonsingular matrices M and N when the matrix F satisfies (F[M,N])[N,M]=F and F[M,N]F (FF[M,N], respectively) is nonsingular, where F[M,N]=Nâ1F#M with F#=FT for real or complex bilinear forms and F#=F¯T for sesquilinear forms. When M=N, our results apply to nonsingular square matrices F. Our assumptions on F, M, and N are in some respects weaker and in some respects stronger than those of previous work on polar decompositions.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 516, 1 March 2017, Pages 126-142
Journal: Linear Algebra and its Applications - Volume 516, 1 March 2017, Pages 126-142
نویسندگان
Xuefang Sui, Paolo Gondolo,