weeks   Week of 5/15--5/21 Week of 5/22--5/28 Week of 5/29--6/04
Sunday   Review the following topics before you come to the first class: system of linear equations, determinant, rank, inverse of matrices, and methods of finding eigenvalues and eigenvectors. Poole, Chapter 1, 2, and 3, plus section 4.1, 4.2, 4.3 of Chapter 4. Review session for Exam 1: 8:30 pm -- 10:00 pm. Finding your favorite applications using techniques of linear algebra.
Monday   Review and present a big picture of linear algebra. When is a square real matrix diagonalizable? Algebraic and Geometric Multiplicity. Diagonalizability of matrices. Unifying theorem of diagonalizability. Poole 4.4. Applications to quadratic forms and geometry. Poole 5.5. Your term project on your favorite real world applications using techniques of linear algebra due today!
Tuesday   Definition and Properties of Similar Matrices. Poole 4.4, Trace=Sum of eigenvalues, Det=Prod of eigenvalues; Proofs of Similar Matrix Properties; Examples of Similar and Non-Similar Matrices. Poole 4.4. Power Method for calculating dominant eigenvalue-eigenvector pairs. Poole 4.5. Exam 1: In Class Linear transformations and their matrix representations, Poole 6.4.
Wednesday   Dot product, norm, length, angle, distance, orthogonality and orthogonal projections, Poole 5.1, 5.2. 1) Applications to Markov chains, 2) Solutions to ODE systems (Read the first one, we will cover the second one), Poole 4.6. The Kernel and Range of linear transformations, Poole 6.5.
Thursday   Gram-Schmidt process, QR factorization, Poole 5.3. Vector spaces and subspaces, Poole 6.1. Inner product spaces, Poole 7.1 and review for final exam.
Friday   Orthogonal diagonalization of symmetric matrix, Poole 5.4. Linear independence, basis, dimension, and 3 basic problems in basis and theorems they lead, Poole 6.2. Last day of class. Final Exam