On Some Characterizations of Hadamard Matrices
| المصدر: | مجلة العلوم الإنسانية والتطبيقية |
|---|---|
| الناشر: | الجامعة الأسمرية الإسلامية زليتن - كليتى الآداب والعلوم |
| المؤلف الرئيسي: | Leghwel, Abd Alrzak M. (Author) |
| المجلد/العدد: | ع24 |
| محكمة: | نعم |
| الدولة: |
ليبيا |
| التاريخ الميلادي: |
2013
|
| الصفحات: | 30 - 51 |
| رقم MD: | 829212 |
| نوع المحتوى: | بحوث ومقالات |
| قواعد المعلومات: | HumanIndex |
| مواضيع: | |
| رابط المحتوى: |
عدد مرات التحميل
3
| المستخلص: |
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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عناصر مشابهة
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On Some Methods of Constructing Hadamard Matrices
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A Remark on the Hadamard Matrices of the Williamson Type
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On Some Applications of Hadamard Matrices
بواسطة: Leghwel, Abd Alrzak M. منشور: (2012) -
On The Excess of Hadamard Matrix
بواسطة: Leghwel, Abd Alrzak M. منشور: (2011) -
The Kronecker Product and The Hadamard Product of Matrices
بواسطة: Abu Shalha, Iman Ali Sulieman منشور: (2000)
