تحليل المصفوفات إلى جداء: مقارنة أداء طرائقها الأساسية ودراسة شروط الحصول على مصفوفات متعامدة نظاميّة بعناصر نسبيّة

باسل عرنوس; عبد الباسط الخطيب; ريم الأحمد

doi:10.5281/zenodo.20964014

Authors

Dr. Basel Alarnous Homs University
Prof. Abdulbasit AlKhatib Homs University
Reem Alahmad Homs University

DOI:

https://doi.org/10.5281/zenodo.20964014

Keywords:

Matrix, Matrix Factorization, QR Factorization, LU Factorization

Abstract

This research conducts a study on matrices and matrix analysis, outlining the essential fundamental definitions required for this purpose.

We provide a historical review of the majority of scholars and researchers who have studied and analyzed matrices, documenting each researcher's methodology. Furthermore, we detail the advantages and disadvantages of each method as applied in previous periods. A comparison was also conducted between QR decomposition and LU decomposition. Finally, we established the necessary conditions for obtaining normalized orthogonal matrices with rational elements.

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