Linear Algebra

• Text: Linear Algebra and its Applications
  3rd Edition (update)
• Author: David Lay
• ISBN-10: 0321287134
• ISBN-13: 978-0321287137

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Ask Thea

1. Install Mozilla from Page for obtaining the Mozilla browser
   It will also be necessary to install math fonts for this browser. Information on how to install these can be found on
   The MathML Fonts Page
   For linux users, the necessary fonts can be found in: mozilla-math.tar.gz (these should be installed in X windows).

Note: Other web pages for this course will not necessarily even show up in other browsers! Once you have installed Mozilla and the fonts, you can check your installation by viewing:

Coverage: chapter 3 and the first three sections of chapter 4.

The MathML Start Page

Use this to check whether MathML is working properly on your web browser. Unfortunately, the Windows version of Mozilla seems to have a bug that will cause it to complain about missing fonts even though the fonts are there (and Mozilla is using them correctly).

Topics covered

1. Introduction:
   • What linear algebra is. Applications.
   • Systems of linear equations
   • Solving such systems: Gaussian elimination
   • Equations with no solutions or an infinite number of solutions.
   • Geometric interpretation
   • Matrices
2. Reduction techniques for matrices
   • Elementary row operations
   • Echelon forms of matrices: pivot elements and columns
   • Row-reduction of matrices
   • Solutions of systems of linear equations via matrices
3. Vectors in 2-space, 3-space
   • Definitions
   • Linear combinations of vectors: the parallelogram rule
   • Span of sets of vectors
   • Vectors equations as shorthand for systems of linear equations.
   • Multiplication of a vector by a matrix
   • The matrix equation Ax=b
   • Homogeneous equations
4. Applications of linear systems.
   • Network flow
5. Linear Independence
6. Linear Transformations: the geometric meaning of matrices
   • Shear transformations
   • Dilations
   • Rotations
7. Determinants
   • Recursive computation
   • Exterior products and tensors
8. Eigenvalues and Eigenvectors
   • Characteristic polynomial
   • Computation of eigenvalues and eigenvectors
   • Geometric significance:
     • Real eigenvalues as dilatons
     • Complex eigenvalue as rotations and dilations
   • Dynamic Equations
9. Inner-product spaces
   • Orthonormal bases of a vector space
   • Orthogonal matrices
   • Orthogonal projection and least-squares approximation

Homework

1. p. 7: 1,2 Due: 1/6/2005
2. p. 53: 1,3. p. 54 12, 16, 17 Due: 1/13/2005
3. p. 79: 3,10. p. 80 23 p. 81 25,30 Due: 1/20/2005
4. p. 106: 16. p. 107 20 Due: 1/20/2005
5. p. 229: 17. p. 230 21, 22, 23 p. 231 30, 31 Due: 2/21/2005

Links

• Math forum on Linear Algebra
• The linear algebra page (from the Mathematical Atlas)
• Maxima Home Page
  Maxima is a free computer algebra system available for Windows and Linux. It can (among many other things) do linear algebra.
• Projective Geometry Page
• Gaussian Elimination

Exam Schedule

1. Exam 1, Week 3
2. Exam 2, Week 6
3. Exam 3, Week 9

Lecture Notes

Lecture notes folder