LINEAR ALGEBRA FOR PATTERN PROCESSING : projection,singular value decomposition, and pseudoinverse

Description

Preface Introduction Linear Space and Projection Eigenvalues and Spectral Decomposition Singular Values and Singular Value Decomposition Pseudoinverse Least-Squares Solution of Linear Equations Probability Distribution of Vectors Fitting Spaces Matrix Factorization Triangulation from Three Views Fundamentals of Linear Algebra Linear Space and Projection Expression of Linear Mapping Subspaces, Projection, and Rejection Projection Matrices Projection Onto Lines and Planes Schmidt Orthogonalization Glossary and Summary Supplemental Notes Problems Eigenvalues and Spectral Decomposition Eigenvalues and Eigenvectors Spectral Decomposition Diagonalization of Symmetric Matrices Inverse and Powers Glossary and Summary Supplemental Notes Problems Singular Values and Singular Value Decomposition Singular Values and Singular Vectors Singular Value Decomposition Column Domain and Row Domain Matrix Representation Glossary and Summary Supplemental Notes Problems Pseudoinverse Pseudoinverse Projection Onto the Column and Row Domains Pseudoinverse of Vectors Rank-Constrained Pseudoinverse Evaluation by Matrix Norm Glossary and Summary Supplemental Notes Problems Least-Squares Solution of Linear Equations Linear Equations and Least Squares Computing the Least-Squares Solution Multiple Equations of One Variable Single Multivariate Equation Glossary and Summary Supplemental Notes Problems Probability Distribution of Vectors Covariance Matrices of Errors Normal Distribution of Vectors Probability Distribution Over a Sphere Glossary and Summary Supplemental Notes Problems Fitting Spaces Fitting Subspaces Hierarchical Fitting Fitting by Singular Value Decomposition Fitting Affine Spaces Glossary and Summary Supplemental Notes Problems Matrix Factorization Matrix Factorization Factorization for Motion Image Analysis Supplemental Notes Problems Triangulation from Three Views Trinocular Stereo Vision Trifocal Tensor Optimal Correction of Correspondences Solving Linear Equations Efficiency of Computation 3D Position Computation Supplemental Notes Problems Fundamentals of Linear Algebra Linear Mappings and Matrices Inner Product and Norm Linear Forms Quadratic Forms Bilinear Forms Basis and Expansion Least-Squares Approximation Lagrange's Method of Indeterminate Multipliers Eigenvalues and Eigenvectors Maximum and Minimum of a Quadratic Form Answers Bibliography Author's Biography Index