MATH 5333-001 Linear Algebra and Matrices

TuTh 04:00-5:20pm, PKH 107

All information is subject to change, please keep yourself informed!

Instructor

Prof. Ren-Cang Li, PKH 445, (817) 272-0548
(send email)

Office hour

TuTh 10-10:50am or by appointment

Handouts

(You'd need a ADOBE reader to preview those handouts.)
  • Course Overview and syllabus, August 25, 2008.
  • MATLAB Primer, August 25, 2008.
  • Definition of a vector space, Sep 25, 2008.
  • Math 5392 APPLIED MATRIX COMPUTING (Low-rank matrix and tensor approximations and their applications), Spring 2009, Sep 25, 2008.

    • Announcements

    Homework Assignments

  • Hw 1: Assigned Aug 26, 2008; due Sept 4, 2008
  • Sec 1.2 -- 1.2.1, 1.2.5, 1.2.8, 1.2.9, 1.2.12, 1.2.13, 1.2.16;
  • Sec 1.3 -- 1.3.2.
  • Hw 2: Assigned Sep 4, 2008; due Sept 11, 2008
  • Sec 2.1 -- 2.1.1(a), 2.1.2, 2.1.3, 2.1.6;
  • Sec 2.2 -- 2.2.1(a), 2.2.5;
  • Sec 2.3 -- 2.3.1(a,b,c), 2.3.3, 2.3.4, 2.3.8;
  • Sec 2.4 -- 2.4.1(c), 2.4.2, 2.4.4, 2.4.6, 2.4.8;
  • Sec 2.5 -- 2.5.2, 2.5.4, 2.5.6;
  • Hw 3: Assigned Sep 11, 2008; due Sept 18, 2008
  • Sec 3.2 -- 3.2.1(b), 3.2.3, 3.2.6;
  • Sec 3.3 -- 3.3.1;
  • Sec 3.4 -- 3.4.1;
  • Sec 3.5 -- 3.5.1(a,b,g,h,k), 3.5.3, 3.5.5, 3.5.8;
  • Sec 3.6 -- 3.6.1, 3.6.5, 3.6.9, 3.6.12.
  • Hw 4: Assigned Sep 18, 2008; due Sep 25, 2008
  • Sec 3.7 -- 3.7.1(d), 3.7.2, 3.7.3, 3.7.9, 3.7.11(a);
  • Sec 3.8 -- 3.8.1, 3.8.3;
  • Sec 3.9 -- 3.9.1, 3.9.2, 3.9.8, 3.9.9, 3.9.10.
  • Hw 5: Assigned Sep 25, 2008; due Oct 2, 2008
  • Sec 3.10 -- 3.10.1, 3.10.2, 3.10.6, 3.10.8;
  • Sec 4.1 -- 4.1.1, 4.1.2, 4.1.6, 4.1.8, 4.1.9, 4.1.11;
  • Hw 6: Assigned Oct 2, 2008; due Oct 9, 2008
  • Sec 4.2 -- 4.2.1, 4.2.3, 4.2.5, 4.2.6, 4.2.7, 4.2.12.
  • Hw 7: Assigned Oct 9, 2008; due Oct 16, 2008
  • Sec 4.3 -- 4.3.2(a), 4.3.5, 4.3.7, 4.3.8, 4.3.11, 4.3.12, 4.3.13(a).
  • Hw 8: Assigned Oct 16, 2008; due Oct 28, 2008
  • Sec 4.4 -- 4.4.4, 4.4.5, 4.4.9, 4.4.16(a), 4.4.17.
  • Sec 4.7 -- 4.7.2, 4.7.6, 4.7.12, 4.7.13.
  • Sec 4.8 -- 4.8.3, 4.8.11, 4.8.12.
  • Hw 9: Assigned Oct 28, 2008; due Nov 6, 2008
  • Sec 5.1 -- 5.1.3, 5.1.5, 5.1.6.
  • Sec 5.2 -- 5.2.3, 5.2.6(d).
  • Sec 5.3 -- 5.3.1, 5.3.2.
  • Sec 5.4 -- 5.4.2, 5.4.5, 5.4.14.
  • Sec 5.5 -- 5.5.1(a,b), 5.5.4, 5.5.5.
  • Sec 5.6 -- 5.6.2, 5.6.4, 5.6.10.
  • Hw 10: Assigned Nov 7, 2008; due Nov 13, 2008
  • Sec 6.1 -- 6.1.1(c), 6.1.6, 6.1.9(a), 6.1.20.
  • Sec 7.1 -- 7.1.1(A,C), 7.1.3, 7.1.4, 7.1.9, 7.1.10, 7.1.17, 7.1.21.
  • Sec 7.2 -- 7.2.2, 7.2.4, 7.2.6, 7.2.12, 7.2.16, 7.2.21, 7.2.22.
  • Hw 11: Assigned Nov 13, 2008; due Nov 20, 2008
  • Sec 7.5 -- 7.5.1, 7.5.3, 7.5.5, 7.5.13.
  • Sec 7.6 -- 7.6.1, 7.6.6.
  • Hw 12: Assigned Nov 20, 2008; due Dec 4, 2008
  • Read Example 7.7.4
  • Sec 7.7 -- 7.7.2, 7.7.6, 7.7.7.
  • Sec 7.8 -- 7.8.1, 7.8.5.

    • Textbook

  • Carl D. Meyer, Matrix Analysis and Applied Linear Algebra, SIAM, 2000.
  • Chapter 1: 1.1, 1.2, 1.3.
  • Chapter 2: 2.1, 2.2, 2.3, 2.4, 2.5.
  • Chapter 3: all sections.
  • Chapter 4: 4.1, 4.2, 4.3, 4.4, 4.7, 4.8, and if time permits, 4.5, 4.6, 4.9.
  • Chapter 5: 5.1, 5.2, 5.3, 5.4, 5.5, 5.6, and if time permits, 5.7, 5.9, 5.10, 5.11, 5.13.
  • Chapter 6: if time permits, 6.1, 6.2.
  • Chapter 7: 7.1, 7.2, 7.5, 7.6, 7.7, 7.8.

    • Exams

  • Mid-Term Exam: Thursday, October 9 (in class). It covers up to Section 4.2 (the section is included).
  • Final Exam: Thursday, December 11, 2-4:30pm. It is comprehensive.

    • To prepare for the exams:

  • One 3"-by-5" formula card (can write on both sides)
  • Working out homework problems.
  • Bring your ID.
    • All of these exams are comprehensive and closed book exams. Calculators are allowed, but work must be showed for credits.

    Computer Resources (optional)

    The computational counterpart of Linear Algebra is Numerical Linear Algebra, a subject that studies how linear algebra problems can be realized in a numerical efficient and stable way, including linear system solving, least squares problems, and eigenvalue computations. Many algorithms that do these are implemented in LAPACK and can also be accessible friendly within MATLAB, a recent version of which is run on mostly computers on campus. MATLAB has an extensive on-line help facility (just type "help" or "help commandname" in MATLAB).

    The Free Software Foundation's Matlab clone called Octave may also be used by those who do not have access to MATLAB. Octave works on Linux and Microsoft Windows.

    Numerical Linear Algebra sits at the heart of pretty much every scientific computation and application. Here at UTA, we have a graduate course MATH 5371 -- Numerical Linear Algebra that teaches the subject. It would be ideally taken after MATH 5333. I would recommend anyone who are interested in scientific computing take MATH 5371, or an equivalent, at some point of his/her education.

    Online Software and Documentation for Linear Algebra Problems

  • LAPACK, state-of-the-art software for dense numerical linear algebra on workstations and shared-memory parallel computers. Written in Fortran.
  • CLAPACK, a C version of LAPACK.
  • LAPACK Manual
  • Templates for the solution of linear systems, a collection of iterative methods, with advice on which ones to use.
  • Templates for the Solution of Algebraic Eigenvalue Problems: A Practical Guide, a collection of iterative methods, with advice on which ones to use.

    • Important Days

  • Monday, August 25, First day of the class
  • Monday, September 1, Labor Day Holiday
  • Wednesday, September 10, Census Date
  • Thursday, October 9, Midterm, in class
  • November 27--30, Thanksgiving Holidays
  • Friday, December 5, Last day of the class
  • Thursday, December 11, 2-4:30pm, Final Exam
    • (see also Academic Calendar)