کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5773212 | 1631076 | 2017 | 10 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Spectrally arbitrary zero-nonzero patterns and field extensions
ترجمه فارسی عنوان
الگوهای طیفی دلخواه صفر غیر صفر و پسوندهای زمینه
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
چکیده انگلیسی
An nÃn matrix pattern is said to be spectrally arbitrary over a field F provided for every monic polynomial p(t) of degree n, with coefficients from F, there exists a matrix with entries from F, in the given pattern, that has characteristic polynomial p(t). Let EâFâK be an extension of fields. It is natural to ask whether a pattern that is spectrally arbitrary over F must also be spectrally arbitrary over E or K. In this article it is shown that if F is dense in K and K is a complete metric space, then any spectrally arbitrary or relaxed spectrally arbitrary pattern over F is relaxed spectrally arbitrary over K. It is also established that if E is an algebraically closed subfield of a field F, then any spectrally arbitrary pattern over F is spectrally arbitrary over E. The 2n Conjecture and the Superpattern Conjecture are explored over fields other than the real numbers. In particular, examples are provided to show that the Superpattern Conjecture is false over the field with 3 elements.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 519, 15 April 2017, Pages 146-155
Journal: Linear Algebra and its Applications - Volume 519, 15 April 2017, Pages 146-155
نویسندگان
Judith J. McDonald, Timothy C. Melvin,