| LEADER |
01823nam a22001937a 4500 |
| 001 |
1587666 |
| 044 |
|
|
|b ليبيا
|
| 100 |
|
|
|9 444253
|a Leghwel, Abd Alrzak M.
|e Author
|
| 245 |
|
|
|a On Some Characterizations of Hadamard Matrices
|
| 260 |
|
|
|b الجامعة الأسمرية الإسلامية زليتن - كليتى الآداب والعلوم
|c 2013
|
| 300 |
|
|
|a 30 - 51
|
| 336 |
|
|
|a بحوث ومقالات
|
| 520 |
|
|
|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.
|
| 653 |
|
|
|a المصفوفات الرياضية
|a العمليات الحسابية
|a مصفوفة هادمارد
|
| 773 |
|
|
|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
|
| 856 |
|
|
|u 1582-000-024-014.pdf
|
| 930 |
|
|
|d y
|p y
|
| 995 |
|
|
|a HumanIndex
|
| 999 |
|
|
|c 829212
|d 829212
|
