Course number: 21810
Meeting Tu Th 9:30 - 10:45
San Diego State University
Last Class: Tu. May 7.
Final Exam: Fri. Th. May 16, 8:00-10:00.
Professor: Mike O'Sullivan
Web page: http://www.rohan.sdsu.edu/~mosulliv/Copurses/matrix13s.html
Office: GMCS #579, ext. 594-6697
Office Hours: Tu Th 1-3:00.
I will usually be available Tu Th 11-12. On other days I am often
available in the afternoon, but it is best to email me in advance to schedule
Horn, Johnson Matrix Analysis Cambridge
University Press, 1st Ed. (1985) or 2nd Ed. (2012).
This is a standard and highly regarded reference on the subject.
While we will not follow it closely, nearly everything we study will
be found, in great depth, in this book.
It is worth having an undergraduate text handy, since Horn's book is
quite intensive. Here are references that I recommend, but
anything you used in a previous course should be sufficient.
Strang, Linear Algebra and Its Applications Any edition.
A widely used, very readable book. I used it to prepare notes on
orthogonal subspaces and the Gram-Schmidt process.
Strang's lectures are also available at MIT's website.
Axler, Linear Algebra Done Right Springer.
I used this for a reference on Jordan canonical form--developing it
without the use of determinants.
A First Course in Linear Algebra.
This is freely available. The web version has embedded Sage code so
that you can do computational experiments within the text of the book.
A good understanding
of linear algebra as in Math 524.
I will assume you've seen the following material.
We will cover it at relatively quickly, and at greater depth.
- Solution of linear systems. Row space, nullspace of a matrix
- Vector spaces, linear independence and bases, subspaces.
- Eigenvalues, eigenspaces, diagonalization, and change of basis.
- Polynomial Ring in One Variable: Divisibility and unique factorization,
the correspondence between factors and roots.
The are numerous interesting topics that we can study in
I expect to introduce the most fundamental results from the following
areas,in roughly the order listed.
If time allows we can explore some topics in more depth.
I'm quite willing to follow the interests of the class.
- Solution of linear systems and matrix algebra.
- Vector spaces and subspaces.
- Orthogonality and Gram Schmidt.
- Unitary similarity.
- Eigenvectors, eigenvalues, diagonalization and Jordan canonical
- Hermitian, and symmetric matrices.
- Location of eigenvalues.
- Positive definite matrices.
- Nonnegative matrices and the Perron-Frobenius theorem.
The course grade will be split roughly evenly between
written homework assignments, and exams.
You are encouraged to work with one another to solve the
problems on the homework, but solutions should be written
I may incorporate problems requiring computations using a mathematics
software package as well.