numerical-linear-algebra

To compute SVD and get a truncated low-rank approximation, use this Skill to decompose your matrix and produce a low-rank representation while reporting the relative Frobenius error across different ranks.

The best way to solve large sparse linear systems with NumPy and SciPy is applying iterative solvers like conjugate gradient (CG) and GMRES, which include basic conditioning and convergence diagnostics for large problems.

Condition number assessment helps by estimating conditioning behavior to choose direct methods, iterative solvers, or regularization and truncation strategies for stable dense or sparse scientific solves.

Yes, you can perform PCA via covariance eigenanalysis for dimensionality reduction, producing interpretable variance explained metrics and component projections from your input matrix.

Yes, this Skill supports Cholesky factorization specifically for symmetric positive definite solves, alongside SVD workflows and eigendecomposition-based insights for numerical matrix analysis.

Iterative solvers like GMRES are used instead of direct methods for sparse matrices to achieve scalable solves on large systems, providing basic conditioning and convergence diagnostics for numerical linear algebra.