INTRODUCION TO LINEAR ALGEBRA (Fall 2008)
Instructor : Dr Gnana Bhaskar Tenali ()
Office : S-317 (Crawford Building) Telephone No: 674-7213
Text Book: Contemporary Linear Algebra
By Howard Anton and Robert C. Busby, John Wiley& Sons, Inc. 2003
Class Timings: M-W 5.00pm – 6.15 pm ; Quad 113
Office Hours: M-W 10.00am -11.00 pm or by Appointment.
Topics
Basic over view of Vectors; Matrices and Matrix Algebra: Inverse of a matrix, Matrices with special forms, Matrix factorizations; LU-Decomposition. Determinants: Properties, Cramer’s Rule.
Systems of linear equations; subspaces and linear Independence; Geometry of Linear Systems; Eigen values and Eigen vectors of Matrices; Hermitian, Unitary and Normal Matrices; Basis and Dimension, Properties of Bases;
The dimension theorem, The rank theorem, the pivot theorem, the projection theorem and its implications, Best approximation and least squares; Orthonormal bases and Gram Schmidt Process; Coordinates with respect to a basis;
Diagonalizability, Orthogonal diagonalizability, Singular Value decomposition;
Linear Transformations: Matrix representation, Kernel and Range, Composition and Invertibility; matrix representation of linear transformations;
General Vector spaces: Vector space axioms, Inner product spaces.
Grading Policy: Final grade is based on the performance in five quizzes, three mid term examinations and a final examination. Each quiz carries 10 points. Each mid term exam carries 50 points. The final exam is for 100 points.
Grading scale: 90%-100% is A; 80%-89% is B; 70% -79% is C; 60% - 69% is D;
Below 60% is F.
There will be only ONE repeat test for those students who may have missed one/two mid term examinations due to valid reasons and with prior permission. This repeat exam would be held one week before the final exam.
Exams Schedule:
Mid Term 1: 9/24/08
Mid Term 2: 10/29/08
Mid Term 3: 11/24/08
Final Examination: December, 8th: 8.30 pm to 10.30 pm.
Homework: I’ll assign plenty of homework after each lecture. Homework is neither collected nor graded. The best way to learn mathematics is to do mathematics. I encourage you to work in groups on the homework. Since you’ll be required to answer the tests without using books, notes, or Calculators, I recommend that you do as much homework as possible without using any of them.
Office Hours: You should make an effort to meet me outside the class for help on homework problems or for assistance in preparing for an examination. Please also feel free to call me to set up an appointment for discussion.
The following online resource is very helpful, when you wish to check the answers to your homework problems. http://www.math.odu.edu/~bogacki/lat/