MATH 63 Summer 2005.
LINEAR ALGEBRA, PART 2.
Professor Weiqing Gu
|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|