Linear Algebra and Matrix Decomposition

This group gathers numerical algorithms whose primary purpose is solving systems of linear equations or decomposing a matrix into a simpler form, including Gaussian elimination, LU decomposition, Cholesky decomposition, QR algorithm, the Gram-Schmidt process, the conjugate gradient method, the Jacobi and Gauss-Seidel iterative methods, successive over-relaxation, the Bareiss algorithm for determinants, and the Kabsch algorithm for finding an optimal rotation matrix between two point sets. Their shared work is manipulating matrices and vectors directly to solve a linear problem, as distinct from finding a root of a general nonlinear function, which belongs to Root-Finding and Optimization, or transforming a signal, which belongs to Signal Processing and Transforms.