linguistic:voice_change, structural:summarization, quality:corruption
Geometric behavior and residual orthogonality

Because each step is taken in the steepest direction, steepest-descent steps alternate between directions aligned with the extreme axes of the elongated level sets. When κ (A) {\displaystyle \kappa (\mathbf {A})} is large, this produces a characteristic zig–zag path. The poor conditioning of A {\displaystyle \mathbf {A} } is the primary cause of the slow convergence, and orthogonality of successive residuals reinforces this alternation.