SUR L’IMPLEMENTION SOUS PYTHON DU PROCEDE D’ORTHOGONALISATION DE GRAM SCHIMDT

This work presents a Python implementation of the Gram-Schmidt orthogonalization process applied to sets of vectors in 2D and 3D Euclidean spaces. The goal is to transform an arbitrary basis into an orthonormal one while preserving the vector space spanned. The approach is illustrated through practical examples, highlighting the usefulness of this method in simplifying the resolution of associated linear systems. Additionally, algorithms are developed to automate the orthogonalization process and solve the systems using substitution methods or triangular matrix techniques. This study demonstrates the efficiency and accuracy of numerical approaches in handling low-dimensional algebraic problems.