Matrix Factorization: A Performance Comparison of its Fundamental Methods and a Study of the Conditions for Obtaining Orthonormal Matrices with Rational Elements

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.