کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
8897957 1631052 2018 17 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
A resolution of Paz's conjecture in the presence of a nonderogatory matrix
ترجمه فارسی عنوان
وضوح حدس پاز در حضور یک ماتریس غالب
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
چکیده انگلیسی
Let Mn(F) be the algebra of n×n matrices over the field F and let S be a generating set of Mn(F) as an F-algebra. The length of a finite generating set S of Mn(F) is the smallest number k such that words of length not greater than k generate Mn(F) as a vector space. It is a long standing conjecture of Paz that the length of any generating set of Mn(F) cannot exceed 2n−2. We prove this conjecture under the assumption that the generating set S contains a nonderogatory matrix. In addition, we find linear bounds for the length of generating sets that include a matrix with some conditions on its Jordan canonical form. Finally, we investigate cases when the length 2n−2 is achieved.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 543, 15 April 2018, Pages 234-250
نویسندگان
, , , ,