MATH V2010:
 Linear Algebra
 Fall 2006

This page is http://www.math.columbia.edu/~bayer/F06/linalg

Section 002 (Bayer)
Tuesdays and Thursdays, 9:10am-10:25pm
304 Barnard Hall

Dave Bayer (x42643, 426 Mathematics, http://www.math.columbia.edu/~bayer)
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Email

For correspondence concerning this course, please use the email address bayer@math.columbia.edu with a subject that includes the text [MATH V2010: Linear Algebra]

Office Hours

Exams

• First Exam, Tuesday, September 26, in class
  
• Second Exam, Thursday, October 19, in class
  
• Third Exam, Thursday, November 16, in class
  
• Final, Thursday, December 21, 9:00am - Noon (projected)
  

These dates do not coincide with any religious holiday which causes suspension of New York City's alternate side parking regulations; see NYC Parking Calendar. Please discuss other conflicts with me well in advance of the exam in question.

Master University Examination Schedule (Projected)
University Academic Calendar

Text

Linear Algebra with Applications, Seventh Edition, by Steven J. Leon. Prentice Hall, 2006, ISBN 0131857851. University bookstore ($125) or AddALL ($46 and up). This semester we will cover chapters 1, 2, 3, 4, 5, 6.

If you can find or happen to have a copy of the 6th edition ($9 and up), then follow the homework recommendations from Spring 2005; homework is not collected. I'm sure that authors are sincere in their revisions of popular textbooks, but publishers also have an economic incentive to invalidate the used textbook market. I'm happy to see this work to your advantage.

Teaching Assistants

The teaching assistant for this course is Helena Kauppila.

Course materials

Since we have four exams, and previous years had three exams, the exams from previous years will not match our schedule. Our first exam will include questions involving the computation of determinants, but not Cramer's rule or the formula for the inverse of a matrix. That material will appear on our second exam.

Homework Assignments

Homework is not collected. Below, I am listing all exercises that you certainly should be able to solve. Use your judgment in deciding which exercises to actually work. It is a good idea to work as many exercises as you can find time to solve; your goal is to achieve fluency, so that you can complete exams comfortably in the time allowed.

You are also invited to look at the more advanced exercises that are not listed.

1. Matrices and Systems of Equations
   1. Systems of Linear Equations. Exercises 1-8
   2. Row Echelon Form. Exercises 1-6
   3. Matrix Algebra. Exercises 1-12
   4. Elementary Matrices. Exercises 1-10
      
      
2. Determinants
   1. The Determinant of a Matrix. Exercises 1-6
   2. Properties of Determinants. Exercises 1-7
   3. Cramer's Rule. Exercises 1-5
      
      
3. Vector Spaces
   1. Definitions and Examples. Exercises 1-6
   2. Subspaces. Exercises 1-11
   3. Linear Independence. Exercises 1-8
   4. Basis and Dimension. Exercises 1-6
   5. Change of Basis. Exercises 1-8
   6. Row Space and Column Space. Exercises 1-4
      
      
4. Linear Transformations
   1. Definition and Examples. Exercises 1-8
   2. Matrix Representations of Linear Transformations. Exercises 1-6
   3. Similarity. Exercises 1-4
      
      
5. Orthogonality
   1. The Scalar Product in Rn. Exercises 1-8
   2. Orthogonal Subspaces. Exercises 1-5
   3. Least Squares Problems. Exercises 1, 3-6
   4. Inner Product Spaces. Exercises 1-3
   5. Orthonormal Sets. Exercises 1-6
   6. The Gram-Schmidt Orthogonalization Process. Exercises 1-6
      
      
6. Eigenvalues
   1. Eigenvalues and Eigenvectors. Exercises 1-4
   2. Systems of Linear Differential Equations. Exercises 1, 2
   3. Diagonalization. Exercises 1-4
   4. Hermitian Matrices. Exercises 1, 2
   5. The Singular Value Decomposition. Exercises 1-4
   6. Quadratic Forms. Exercises 1-3
   7. Positive Definite Matrices. Exercises 1-4
      
      

Calendar