numerical-linear-algebra

What problem does it solve?

This Skill helps you analyze and compute with matrices by enabling stable decomposition, dimensionality reduction, and efficient linear system solves for both dense and sparse scientific problems.

Core Features & Use Cases

• Matrix decompositions: compute SVD, eigendecomposition, and Cholesky factorization to understand structure and recover low-rank representations.
• Dimensionality reduction: run PCA via covariance eigenanalysis for interpretable variance explained and component projections.
• Scalable solvers: apply iterative methods like conjugate gradient (CG) and GMRES for large sparse systems, including basic conditioning and convergence diagnostics.
• Conditioning insights: estimate condition number behavior to choose direct methods, iterative solvers, or regularization/truncation strategies.

Quick Start

Use the numerical-linear-algebra Skill to compute an SVD of your matrix and produce a truncated low-rank approximation while reporting relative Frobenius error across different ranks.