This page will be updated frequently with current and upcoming topics.
Schedule
Date  Topics  References  Out  Due 

March 26  Introduction, class objectives and policies 
 HW 0  
March 28  Handson Introduction to Matlab  HW 0  
April 2 
 HW 1  
April 4 
 
April 9 
 HW 2  HW 1  
April 11 
 
April 16  Orthogonality 
 HW 2  
April 18  SVD 
 
April 23  Eigenvalue problem continued; PCA 
 HW 3  
April 25 
 
April 30 
 Project Proposal  HW 3  
May 2 
 
May 7  No class 
 Project Proposal  
May 9  No class 
 
May 14 
 
May 16 
 
May 21  Project presentations:

 
May 23  Project presentations:

 
May 28  Project presentations:

 
May 29  Final Project due 
 Final Project 
Syllabus
 Matlab, part I:
basic arithmetic; vectors and matrices; matrix arithmetic; control structures; input/output; scripts and functions.
 Linear Algebra, solving Ax=b:
row and column picture; Gaussian elimination; matrix inverse; GaussJordan; LU factorization and its applications; vector spaces; geometric interpretations of nullspace, rowspace, columnspace and left nullspace of a matrix; algorithms to compute the nullspace, rowspace, columnspace and left nullspace of a matrix.
 Matlab, part II:
data structures; 1D plotting; 2D images; 3D surfaces; GUI programming.
 Leastsquares estimation:
applications: linear and nonlinear regression, data fitting; the calculus view: system of normal equations; the linear algebra view: geometric interpretation of leastsquares fitting via projection onto the columnspace.
 Singular Value Decomposition:
orthogonal bases and matrices; geometric interpretation of SVD; applications: dimensionality reduction, rank computation; least squaresfitting via SVD: the pseudoinverse.
 Eigenvectors and eigenvalues:
discussion of special cases: projection matrix, permutation matrix, triangular matrix; characteristic equation; remarks on iterative methods for eigendecomposition; application: solving recursive matrix equations; application: Principal Component Analysis; PCA via SVD; eigenfaces for face recognition.
 One dimensional optimization:
golden section search; Newton's method.
 Multidimensional unconstrained optimization:
steepest descent, discussion of methods for line search; Newton's method; conjugate gradient (geometric interpretation, derivation for quadratic function, generalization to arbitrary function).
 Constrained optimization:
method of Lagrange multipliers.
 Linear programming:
simplex algorithm.