21 B
Mathematics Math21b Spring 2015
Linear Algebra and Differential Equations
Exhibit: Kyle numbers
Course Head: Oliver Knill
Office: SciCtr 432

Kyle numbers

Kyle Burke wrote the first solutions to the Bretscher book. Maybe to make the solutions a bit more personal or maybe as a joke, he introduced an ``easter egg" and called some numbers "Kyle numbers". Suddenly, students were talking about these mysterious "Kyle numbers" and the instructors (who would of course solve the problems themselves and not look up the solutions) would have no clue!
Kyle Burke's website at Plymouth State University.

Here is how it goes: if you see a matrix like
    1  2  3  4  5   
    2  4  6  8 10
    3  6  9 12 15
you can often immediately write down the kernel of the matrix by placing numbers above the columns. They tell how to add the columns up to get zero. For example, in the case of the above matrix, one can see

    3  0 -1  0  0

    1  2  3  4  5
    2  4  6  8 10
    3  6  9 12 15
because 3 times the first column minus the third column is zero. The matrix indeed has the kernel [3,0,-1,0,0]^T. Similarly, [2,-1,0,0,0]^T,[4,0,0,-1,0]^T,[5,0,0,0,-1] are kernel vectors. These 4 vectors form a basis of the 4 dimensional kernel.
The numbers are now acknowledged in the later editions of the book by Otto Bretscher. In edition 4 for example, it appears on page 131.

Since Oliver also once worked on the solutions, he can count the number of occurrences of "Kyle". In the source solution file of 2008, it appears 15 times:
Please send questions and comments to
Math21b Harvard College/GSAS: 1771, Exam group 3| Oliver Knill | Spring 2015 | Department of Mathematics | Faculty of Art and Sciences | Harvard University, [Canvas], [ISites]. Bookmark| Twitter