(I will try to post notes here right before lecture.)

This concise review of linear algebra summarizes some of the background needed for the course.

See also some notes on basic matrix-vector manipulations.

Notes 01, Introduction

**I. Vector spaces and linear representations
**Notes 02, first look at linear representations

Notes 03, linear vector spaces

Notes 04, norms and inner products

Notes 05, linear approximation

Notes 06, orthogonal bases

Notes 07, nonorthogonal bases

**II. Regression using least squares**

Notes 08, regression as a linear inverse problem and least squares

the code in regression_example.m solves some toy problems

Notes 09, least-squares in a Hilbert space

Notes 10, reproducing kernel Hilbert spaces

Notes 11, kernel regression, Mercer’s theorem

**III. Solving and analyzing least squares problems**

Notes 12, symmetric systems of equations

Notes 13, the SVD and least-squares

Notes 14, stable least-squares reconstruction

Notes 15, matrix factorization

Notes 16, steepest descent and conjugate gradients

**IV. Statistical estimation and classification**

Notes 17, probability review, WLLN, and MMSE estimation

Notes 18, Gaussian estimation, Gaussian graphical models

Notes 19, maximum likelihood estimation

Notes 20, consistency and the Cramer-Rao lower bound

Notes 21, Bayesian estimation

Notes 22, the Bayes classifier, nearest neighbor

Notes 23, empirical risk minimization

Notes 24, logistic regression

**V. Further topics**

Notes 25, gradient descent

Notes 26, PCA and NNMF

Notes 27, Gaussian mixture models

Notes 28, hidden Markov models