Syllabus for M340L

Matrices and Matrix Calculations

Text: David C. Lay, Linear Algebra and its Applications, 4th ed.

Prerequisite: One semester of calculus, with grade of at least C-, or consent of instructor.

Background: M341 (Linear Algebra and Matrix Theory) and M340L (Matrices and Matrix Calculations) cover similar material. However, the emphasis in M340L is much more on calculational techniques and applications, rather than abstraction and proof. (M341 is the preferred linear algebra course for math majors and contains a substantial introduction to proof component.) Credit cannot be received for both M341 and M340L.

Course Content: Read the "Note to the Instructor" at the beginning of the book. The core of M340L is indeed the "core topics" listed on pages ix-x, plus sections 3.1 and 3.2. Various faculty members disagree strongly about which of the remaining "supplementary topics" and "applications" are most important; use your own judgment. You will probably have time for about half a dozen of these supplementary topics and applications.

The syllabus covers the essentials of all seven chapters of Lay, namely

  1. Linear Equations in Linear Algebra,
  2. Matrix Algebra,
  3. Determinants,
  4. Vector Spaces,
  5. Eigenvalues and Eigenvectors,
  6. Orthogonality and Least Squares, and
  7. Symmetric Matrices and Quadratic Forms.

Each section is designed to be covered in a single 50-minute lecture. However, in practice chapters 1 - 3 should be covered more quickly (a bit slower on the last 3 sections of chapter1), allowing more time for chapters 4-7. Most incoming M340L students are already quite adept at solving systems of equations, and it is important to move quickly at the beginning of the term to material that does challenge them, reserving time to tackle the more difficult vector space concepts of chapter 4. Many of the essential concepts, such as linear independence, are covered twice: once in chapter 1 for Rn, then again in chapter 4 for a general vector space.

Computers: Linear algebra lends itself extremely well to computerization, and there are many packages that students can use. Once students have learned the theory of row-reduction and matrix multiplication (which they pick up very quickly), they should be encouraged to use Maple, Matlab, Mathematica, or a similar package. There are also many "projects" on the departmental computers that students can learn from. Many concepts in the book, especially in the later chapters (e.g., understanding the long-time behavior of a dynamical system from its eigenvalues), can be absorbed quite easily through numerical experimentation.

Revised by Gary Hamrick, June, 2003