Optimum Signal Processing 2002 – 2007 SVD , PCA , KLT , CCA , and All That

1 Vector and Matrix Norms, 2 2 Subspaces, Bases, and Projections, 3 3 The Fundamental Theorem of Linear Algebra, 7 4 Solving Linear Equations, 7 5 The Singular Value Decomposition, 13 6 Moore-Penrose Pseudoinverse, 18 7 Least-Squares Problems and the SVD, 20 8 Condition Number, 22 9 Reduced-Rank Approximation, 23 10 Regularization of Ill-Conditioned Problems, 29 11 SVD and Signal Processing, 30 12 Inverse Filter Design, 36 13 Least-Squares Linear Prediction, 38 14 MA and ARMA modeling, 40 15 Karhunen-Loève Transform, 45 16 Principal Component Analysis, 47 17 SVD Signal Enhancement, 52 18 Structured Matrix Approximations, 57 19 Matrix Pencil Methods, 60 20 QR Factorization, 64 21 Canonical Correlation Analysis, 66 References, 72