کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
8953093 1645907 2018 24 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Inertia, positive definiteness and ℓp norm of GCD and LCM matrices and their unitary analogs
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Inertia, positive definiteness and ℓp norm of GCD and LCM matrices and their unitary analogs
چکیده انگلیسی
Let S={x1,x2,…,xn} be a set of distinct positive integers, and let f be an arithmetical function. The GCD matrix (S)f on S associated with f is defined as the n×n matrix having f evaluated at the greatest common divisor of xi and xj as its ij entry. The LCM matrix [S]f is defined similarly. We consider inertia, positive definiteness and ℓp norm of GCD and LCM matrices and their unitary analogs. Proofs are based on matrix factorizations and convolutions of arithmetical functions.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 558, 1 December 2018, Pages 1-24
نویسندگان
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