Applied Linear Algebra
MA 590 (Special Topics), CRN 11276
  Fall 2013

Syllabus


About the Course This course provides an introduction to the theory and methods of applied linear algebra. The goal is to bring out the fundamental concepts and techniques that underlie the many ways in which linear algebra is used in applications. The course is suitable for graduate students in Mathematics, Computer Science and other disciplines who wish to obtain deeper insights into this important subject.

Topics to be covered are:
  1. General introduction and review of basic concepts (vector spaces, linear independence, bases, dimension, subspaces).
  2. Linear transformations and matrices (linear transformations, matrix representations, range and null space, invertibility, solution of linear equations, eigenvalues and eigenvectors, determinants, similarity transformations, spectral invariance, diagonalizability). 
  3. Norms and inner products (norms, equivalence of norms, limits and convergence of sequences, inner products, orthogonality, orthonormal bases, orthogonalization).
  4. Orthogonal complements, orthogonal projections, and the representation theorem.
  5. Linear transformations on inner-product spaces (adjoint transformations, matrix transpose and Hermitian transpose, linear equations revisited, linear functionals and dual spaces).
  6. Symmetric and positive-definite transformations (symmetric transformations, symmetric and Hermitian matrices, linear equations revisited, orthonormality of eigenvectors, spectral theorem, positive and positive-definite transformations and matrices, quadratic forms).
  7. Unitary transformations, orthogonal and unitary matrices.
  8. Jordan, Schur and singular value decompositions.
  9. Matrix functions, exponentials and systems of differential equations (as time permits).

Recommended background: undergraduate-level linear algebra.


Exams
 The mid-term will take place on Tuesday, October 15, the mid-point of the course. The final will take place on Tuesday, December 17, the last day of the course.

Exam makeup policy: Makeup exams will be allowed only in the event of a documented medical or other unforeseen emergency. You are responsible for avoiding foreseeable conflicts with the exams.


Homework
 Homework assignments will normally be given each Tuesday, to be turned in the next Tuesday.

To receive full credit, homework assignments must normally be handed in when due. Assignments may be turned in late with a valid excuse; this should be discussed with me and approved in advance if possible or otherwise at the earliest opportunity. 


Lecture Attendance
 This will not be monitored but is expected. You are responsible for knowing everything said or covered in class.


Collaboration
 You are welcome, even encouraged, to collaborate on the homework, but you are expected to understand everything that you hand in. Collaboration is not allowed on the exams.


Academic Honesty
 You are expected to be aware of and familiar with WPI's Academic Honesty policies, which can be found at http://www.wpi.edu/offices/policies/honesty/. Cheating or helping others on the exams will be prosecuted according to the university's policy. 


Students with Disabilities  If you need course adaptations or accommodations because of a disability, or if you have medical information to share with me, please make an appointment with me as soon as possible.  Students with disabilities who believe that they may need accommodations in this or another class are encouraged to contact the Disability Services Office (DSO) as soon as possible to ensure that such accommodations are implemented in a timely fashion. The DSO is located in the Student Development and Counseling Center. The phone number is 508-831-4908; the e-mail address is dso@wpi.edu.