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MATH 405/505 Linear Algebra
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COURSE GOALS: To comprehend fundamental concepts and theorems of Linear Algebra, to be proficient in
performing related computations on a small scale. Proficiency is to be achieved through homework exercises and in-class
exams.
TEXTBOOKS: Linear Algebra, A Modern Introduction by David Poole (3rd Edition)
OUTLINE: Fundamentals of eigenvalues/eigenvectors, diagonalization, orthogonality, norms, vector spaces, bases,
transformation, and least square approximation
ATTENDANCE REGULATIONS: Class attendance is a privilege as well as an obligation. All students are expected to
attend classes punctually. Failure to come to class three times without proper written notice (court appearance paper or
Doctor’s excuse) will result in exclusion from the final exam. One occasion of cheating on the attendance sheet will result
in 2-point deduction from the overall score for all persons involved. Please be warned that this will be strictly enforced
without further notice.
HOMEWORK POLICY: The homework assigned during a particular class is due back at 3:50pm one week later unless
otherwise noticed. Graduate students have extra problems to work on. Homework will be partially graded. If homework is
turned in within 48 hours after the due time, the student only receives 50% of the credit; if is submitted beyond 48 hours
after the due time, no credit will be awarded.
EXAMINATIONS: There will be two tests and a comprehensive final exam. Graduate students have an extra problem.
In case of a missing test, a valid excuse is required to have your next test double-counted. A forged excuse or an
unexcused absence from an exam will result in a score of zero.
GRADE DETERMINATION POLICY: Communication between students during a test is strictly prohibited. Failure to
abide by testing rules is considered an honor code violation and will result in a score of zero. The overall grade is a
weighted average of all activities: Test 1 (25%), Test 2 (25%), Homework sets (20%), and final (30%).
STUDENTS NEEDING SPECIAL ACCOMODATIONS: Students requiring special accommodation for testing based
on an established disability record should discuss it with the instructor during the first week of class. A synchronized test
will be given at the Disability Testing Center that provides the requisite accommodations. Administration of a separate
test, which will be different and could be harder, is contingent upon the approval by the instructor, and requires a written
request to the instructor 48 hours ahead of the testing time.
RETENTION POLICY ON GRADED MATERIALS AND GRADE REPORT: All students are required to return
the graded test papers without alteration back to the instructor after reviewing them. All test papers will be reviewed
before reporting a final grade of a student to the Registrar’s office.
HONOR CODE: In accordance with the Academic Honor Code, students pledge the following, “Being a student of
higher standards, I pledge to embody the principles of academic integrity.” Any academic misconduct in violation of the
Honor Code will carry a minimum penalty of an “F” for the assignment in question. The instructor reserves the right to
enforce a more stringent penalty. For more details on the honor code, refer to http://www.latech.edu/documents/honorcode.pdf.
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Course Content and Homework Problems
Topic
4.3 Eigenvalues and Eigenvectors of n x n matrices
4.4 Similarity and Diagonalization
4.5 Iterative method for computing eigenvalues
5.1 Orthogonality
5.2 Orthogonal Complements and Projections
5.3 Gram-Schmidt process and the QR factorization
5.4 Orthogonal diagonalization of symmetric systems
Test 1
6.1 Vector Spaces and Subspaces
6.2 Linear Independence, Basis, and Dimension
6.3 Change of Basis
6.4 Linear Transformations
6.5 Kernel and Range of a linear transformation
6.6 Matrix of a Linear Transformation
Test 2
7.1 Inner Product Spaces
7.2 Norms and Distance Functions
7.4 The singular value decomposition
Comprehensive Final
Assignments