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01843nam a22002057a 4500 |
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| 041 |
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|a eng
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| 044 |
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|b ليبيا
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| 100 |
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|9 444253
|a Leghwel, Abd Alrzak M.
|e Author
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| 245 |
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|a On Some Characterizations of Hadamard Matrices
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| 260 |
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|b الجامعة الأسمرية الإسلامية زليتن - كليتى الآداب والعلوم
|c 2013
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| 300 |
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|a 30 - 51
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| 336 |
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|a بحوث ومقالات
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| 520 |
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|b The purpose of this paper is to present some interesting and basic properties of some characterizations of Hadamard matrices . To accomplish this goal we begin with the development of some basic tools. These tools include a study of the class of positive definite matrices and an expansion formula for the determinant of a partitioned matrix . Using these tools a pivotal result due to Hadamard (1893) , known as the Hadamard determinant inequality is established. The Hadamard determinant inequality is used to present a major result due to Hadamard (1893) and is the main theorem of this paper, namely a characterization of a Hadamard matrix as a best d-optimal matrix in a suitable class of matrices. We conclude this paper by proving a necessary condition that is satisfied by the order n of a Hadamard matrix . It is shown that a necessary condition for a Hadamard matrix of order n to exist is that n=1 , n= 2 or n be congruent to zero mod 4.
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| 653 |
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|a المصفوفات الرياضية
|a العمليات الحسابية
|a مصفوفة هادمارد
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| 773 |
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|4 العلوم الإنسانية ، متعددة التخصصات
|6 Humanities, Multidisciplinary
|c 014
|l 024
|m ع24
|o 1582
|s مجلة العلوم الإنسانية والتطبيقية
|t Journal of Humanities and Applied Sciences
|v 000
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| 856 |
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|u 1582-000-024-014.pdf
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| 930 |
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|d y
|p y
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| 995 |
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|a HumanIndex
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| 999 |
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|c 829212
|d 829212
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