Chapter 11: SciPy Linear Algebra

This chapter covers SciPy's linear algebra capabilities, including dense matrix decompositions, eigenvalue problems, matrix functions, sparse matrix operations, and practical applications like PDE discretization and graph algorithms.

11.1 Overview

• SciPy vs NumPy Linalg
• Module Organization

11.2 Dense Matrix Operations

• LU Decomposition
• Cholesky Decomposition
• QR Decomposition
• Schur Decomposition
• Hessenberg Form

11.3 Eigenvalue Problems

• General Eigenvalues
• Symmetric Eigenvalues
• Generalized Eigenvalues

11.4 Matrix Functions

• Matrix Exponential
• Matrix Logarithm
• Matrix Square Root
• Fractional Power

11.5 Sparse Matrix Basics

• Why Sparse Matrices
• Storage Formats
• Creating Sparse Matrices
• Format Conversion

11.6 Sparse Matrix Operations

• Arithmetic Operations
• Matrix Multiplication
• Slicing and Indexing

11.7 Sparse Solvers

• Direct Solvers
• Iterative Solvers
• Preconditioning
• Sparse Eigenvalues

11.8 Special Matrices

• Toeplitz and Circulant
• Block Matrices
• Companion Matrix

11.9 Best Practices

• Format Selection Guide
• Performance Tips

11.10 Applications

• PDE Discretization
• Graph Algorithms
• Sparse Matrix Applications