کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4599890 1336826 2013 18 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Inner products on the space of complex square matrices
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Inner products on the space of complex square matrices
چکیده انگلیسی
In this paper we study the problem of finding explicit expressions for inner products on the space of complex square matrices Mn(C). We show that, given an inner product 〈⋅,⋅〉 on Mn(C), with some conditions, there exist positive matrices Aj and Bj∈Mn(C), for j=1,2,…,m such that〈X,Y〉=∑j=1mtrace(Y⁎AjXBj), for all X,Y∈Mn(C). However, we show that the result does not hold for all inner products. In fact, if the above expression does not hold, we show that there exist positive matrices Aj and Bj∈Mn(C), for j=1,2,…,m such that〈X,Y〉=−trace(Y⁎A1XB1)+∑j=2mtrace(Y⁎AjXBj), for all X,Y∈Mn(C).
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 439, Issue 11, 1 December 2013, Pages 3620-3637
نویسندگان
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