Vaughn Climenhaga

Assistant Professor
Department of Mathematics
University of Houston

Math 4377/6308

Advanced Linear Algebra I
Fall 2013

End-of-term announcements:
  1. Office hours for December 2 and 4 are cancelled, as I will be out of town at a conference.  Lectures will continue as normal, with guest lecturers.  HW 11 should still be turned in during lecture on Wednesday, December 4.

  2. The final exam is Friday, December 13, from 5-8pm, in the usual classroom (F 154).  It will be similar in structure to the two tests and is cumulative -- all topics covered in lecture this semester are fair game.

  3. The week of the final exam, there will be a review session on Tuesday, December 10 from 2-3pm in PGH 646.  This will be an informal review session -- I will not prepare a presentation, but will be available to answer questions and review details of homework assignments, tests, etc.

  4. Office hours the week of the final exam will be 10am-12pm Thursday, Dec 12 and 2-3pm Friday, Dec 13.  If you have questions and cannot come during these times or to the review session, email me and I will either answer your questions via email or will set up an alternate time to meet.

Vaughn Climenhaga
  • Office: 651A PGH
  • Office hours:  Mondays and Wednesdays, 2-3pm or by appointment 
  • Email: climenha [at]

Course description:
  • Lectures:  Mondays and Wednesdays, 4-5:30pm, room F 154
  • Textbook:  Linear Algebra and its Applications, second edition, by Peter D. Lax.  (Wiley, 2007)
  • Course syllabus
  • The course will cover Chapters 1-7 of the textbook.  Topics include vector spaces and linear maps from the abstract point of view; determinant, trace, and spectral theory (eigenvalues, eigenvectors) of linear maps; and the structure of Euclidean space.  Some topics appear similar to those in Math 2331, but in this course we will take a more abstract approach and discuss the topics in more generality and rigour.  In particular, note that this is a proof based course.
In addition to the office hours listed above, you are encouraged to make use of the tutoring resources available to you at CASA.

You may occasionally find it helpful to have access to other resources
that give a more expanded and detailed presentation of various topics than is available in Lax’s book or in the lecture notes. To this end I suggest the following list of external references, which are freely available online.
  • “A First Course in Linear Algebra”, by Robert A. Beezer, University of Puget Sound. Long and comprehensive (1027 pages). Starts from the very beginning: vectors and matrices as arrays of numbers, systems of equations, row reduction. Organisation of book is a little non-standard: chapters and sections are given abbreviations instead of numbers.
  • “Linear Algebra”, by David Cherney, Tom Denton, and Andrew
    Waldron, UC Davis. 308 pages. Covers similar material to Beezer's book.
  • “Linear Algebra”, by Jim Hefferon, Saint Michael’s College. 465
    pages. Again, starts from the very beginning. 
  • “Linear Algebra as an Introduction to Abstract Mathematics”, by
    Isaiah Lankham, Bruno Nachtergaele, and Anne Schilling, UC Davis.  247 pages. More focused on abstraction than the previous three references, and hence somewhat more in line with the present course.
  • “Linear Algebra Done Wrong”, by Sergei Treil, Brown University.  276 pages. Starts from the beginning but also takes a more abstract view.

The books listed above can all be obtained freely via the links provided.  Another potentially useful resource is the series of video lectures by Gilbert Strang from MIT’s Open CourseWare project.

Lecture notes

Test 1 materials

 - Review sheet
 - An old test for practice
 - Solutions to the practice test
 - Test 1 with solutions

Test 2 materials

 - Review sheet
 - An old test for practice
 - Solutions to the practice test
 - Test 2 with solutions

(Caution: the old test does not include questions on eigenvalues, eigenvectors, or determinants, all of which are included in the material for this test.)

Final exam materials

 - Review sheet
 - An old exam for practice (I do not have written solutions for this exam)


HW 1 (due Wed Aug 28)
 - Solutions

HW 2 (due Wed Sep 4)
 - Solutions

HW 3 (due Wed Sep 11)
 - Solutions

HW 4 (due Wed Sep 18)
 - Solutions

HW 5 (due Wed Sep 25)
 - Solutions

HW 6 (due Wed Oct 9)
 - Solutions

HW 7 (due Wed Oct 16)
 - Solutions

HW 8 (due Wed Oct 23)
 - Solutions

HW 9 (due Wed Nov 13)
 - Solutions

HW 10 (due Wed Nov 20)
 - Solutions

HW 11 (due Wed Dec 4)
 - Solutions