Implementation of the Gram-Schmidt Orthogonalization Process

The primary objective of this program is to implement the Gram-Schmidt orthogonalization process. This algorithm transforms a set of linearly independent vectors into an orthogonal vector set, which is crucial for scientific research and engineering design. The program enables users to efficiently execute this process while ensuring computational accuracy and performance. Users can customize the number and dimensions of input vectors through parameter configuration. The implementation involves key steps: projecting each vector onto the orthogonal complement of the subspace spanned by previous vectors, followed by normalization. The program outputs the orthogonalized vectors along with relevant metrics such as orthogonality verification. Applicable in both academic and industrial contexts, this tool facilitates complex vector space operations through a robust algorithmic implementation that handles numerical stability considerations like reorthogonalization when necessary.