11. Singular Value Decomposition and Matrix Analysis

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11.1 Singular Value Decomposition

Singular Values and Singular Vectors

Full and Reduced SVD

Geometric Interpretation of SVD

SVD and the Four Fundamental Subspaces

Computing the SVD

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11.2 Applications of SVD

Low-Rank Approximation and Eckart-Young Theorem

Moore-Penrose Pseudoinverse

Image Compression

Principal Component Analysis

Latent Semantic Analysis

Noise Filtering and Denoising

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11.3 Matrix Norms and Conditioning

Vector Norms

Induced and Frobenius Matrix Norms

Spectral Radius

Condition Number

Sensitivity and Error Bounds

Numerical Stability of Algorithms

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