sed vs ged

Practical ApplicationsStandard Decomposition ($A v = \lambda v$):Principal Component Analysis (PCA): Maximizes variance along directions in a single covariance matrix $\Sigma$.Markov Chains: Finding stationary distributions via transition matrices.Graph Theory: Spectral clustering using the unnormalized Graph Laplacian ($L = D - W$).Generalized Decomposition ($A v = \lambda B v$):Linear Discriminant Analysis (LDA): Maximizes between-class variance $S_B$ while minimizing within-class variance $S_W$, solving $S_B v = \lambda S_W v$.Vibrational Mechanics / Structural Dynamics: Solving equations of motion $K u = \omega^2 M u$, where $K$ is the stiffness matrix, $M$ is the mass matrix, and $\omega^2$ represents the natural frequencies.Canonical Correlation Analysis (CCA): Finding maximum cross-covariance between two sets of variables relative to their internal covariances.