کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
9498169 1631191 2005 12 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On the Wedderburn-Guttman theorem
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
On the Wedderburn-Guttman theorem
چکیده انگلیسی
Let A be a u by v matrix of rank a, and let M and N be u by g and v by g matrices, respectively, such that M′AN is nonsingular. Then, rank(A − N(M′AN)−1M′A) = a − g, where g = rank(AN(M′AN)−1M′A) = rank(M′AN). This is called Wedderburn-Guttman theorem. What happens if M′AN is rectangular and/or singular? In this paper we investigate conditions under which the regular inverse (M′AN)−1 can be replaced by a g-inverse (M′AN)− of some kind, thereby extending the Wedderburn-Guttman theorem. The resultant conditions look similar to those arising in seemingly unrelated contexts, namely Cochran's and related theorems on distributions of quadratic forms involving a normal random vector.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 410, 15 November 2005, Pages 267-278
نویسندگان
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