دراسة مقلوب مصفوفة متماثلة الإيجابية وطيفها
Abstract
في هذا البحث وصف للمصفوفات الموجبة، موجبة نصفية التحديد، موجبة التحديد، متماثلة الإيجابية متماثلة الإيجابية بدقة، والشروط التي يجب أن يحققها تابع لعدة متحولات للحصول على نهاية صغرى عند نقطة المبدأ.
تم البرهان على أنه إذا كانت المصفوفة متماثلة الإيجابية، والتي شكلها التربيعي يصل نهاية صغرى تساوي الصفر عند نقطة المبدأ، فإن مصفوفة المقلوب تكون أيضاً مصفوفة متماثلة الإيجابية، ومقلوب مصفوفة متماثلة الإيجابية، والتي شكلها التربيعي لا يملك نهاية صغرى تساوي الصفر عند المبدأ، ليست بالضرورة مصفوفة متماثلة الإيجابية.
This piece of research presents positive, positive semi-definite, copositive strictly copositive matrices, and conditions for achieving the minimum value function at origin point.
It has been proved that the copositive matrix, which its quadratique form has minimum zero at the origin point then its inverse is a copositive matrix, and the copositive matrix which its quadratique don’t have minimum zero at the origin point then its inverse is not a necessarily copositive matrix.
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