Exploring the Techniques of Lagrangian Reduction and Congruence Transformation in Matrix Analysis

Author(s)	Ms. Vida Sanbohiba Yiran, Prof. Natalia G. Mensah, Dr. Henrietta Nkansah, Mr. Ransford Ganyo
Country	Ghana
Abstract	The study explores special cases of symmetric matrices, quadratic forms, triangular matrices, Hermitian, and skew-Hermitian matrices by employing the techniques of Lagrangian reduction and congruence transformation to determine the congruence of two matrices. The study thus provides insights into the intricacies of these matrices and their quadratic forms. The findings of this study contribute to the broader field of matrix analysis and offer potential application to various areas of science and engineering.
Keywords	Lagrangian reduction, Congruence transformation, Hermitian and skew-Hermitian Matrices, Quadratic forms, Symmetric Matrices, Triangular Matrices
Field	Physical Science
Published In	Volume 7, Issue 3, May-June 2025
Published On	2025-06-28
DOI	https://doi.org/10.36948/ijfmr.2025.v07i03.48795
Short DOI	https://doi.org/g9rn4h

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International Journal For Multidisciplinary Research