21 B
Mathematics Math21b Spring 2009
Linear Algebra and Differential Equations
Course Head: Oliver Knill
Office: SciCtr 434
Send questions of potential general interest to

See also the FAQ from previous years: 2008, 2007.

Question:What are "Kyle numbers"? Answer: The book (and especially the solution book) mentions Kyle numbers. They are a short cut to compute the kernel, especially for 2 times 2 matrices. If a 2 x 2 matrix is not invertible, the two columns have to be parallel. For
  A =   | 2   -4 | 
        | 4   -8 |
for example, we see that the second column is -2 times the first column. The Kyle numbers are 1, 2 because adding the first to 2 times the second column gives zero. So that [1,-2]^T is in the kernel. Its better to stick to row reduction to compute the kernel since it is easy (especially for larger matrices) to get only part of the kernel.
Please send questions and comments to
Math21b (Exam Group 1)| Oliver Knill | Spring 2009 | Department of Mathematics | Faculty of Art and Sciences | Harvard University