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Register a new userDeveloping Lower Bounder for The Spectral Radius of a Numerical Matrix
تحسين الحدود الدنيا لنصف القطر الطيفي لمصفوفة عددية
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لتكن A مصفوفة حقيقية، بحيث rank A = m ≥ 2, و ليكن (ρ (A نصف القطر الطيفي للمصفوفة A. و في حال كون rank A =m=2 فإن كلا من المتراجحتين (١) و (٢) تؤول إلى مساواة. بالإضافة إلى ذلك فإنه تم تعميم هذه النتائج في حالة كون A مصفوفة مربعة من المرتبة n و التي مداخلها القطرية أعداد عقدية.
This paper is concerned with the calculation of the spectral radius of an arbitrary real matrix A If rank A = m = 2 then (١) and (٢) are equalities. In addition, we provide the numerical radius r(A) of an n×n matrix whose diagonal entries are complex numbers.
References used
F. R. Gantmacher ,The theory of matrices, Chelsea, New York1977
R.A. Horn and C.L. Giles, An experimental comparison of recurrent neural networks, MIT Press1995
M.Marcus and H. minc, A survey of Matrix theory and Matrix inequalities, Dover, New York1964
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