What are Kyle Numbers and how do you compute them?

[mahrap]

My linear algebra uses "Kyle Numbers" to compute some kernels. But it does not elaborate on what they are and how they are used to compute the kernel? Please help.

 

[fzero]

I found http://www.math.harvard.edu/archive/21b_spring_09/faq.html. The name isn't standard, but the concept seems to make sense. Post back if the explanation on that page is insufficient.

 

[mahrap]

I found http://www.math.harvard.edu/archive/21b_spring_09/faq.html. The name isn't standard, but the concept seems to make sense. Post back if the explanation on that page is insufficient.

I understand the concept. But do you think there is an algorithm to compute these numbers? Or should I just find the kernel by sticking with row reduction?

 

[fzero]

I understand the concept. But do you think there is an algorithm to compute these numbers? Or should I just find the kernel by sticking with row reduction?

It would be fine to stick with row reduction. For 2x2 matrices with rational entries, you could come up with an algorithm to find the smallest integers $(k_1,k_2)$ such that the column vectors satisfy $k_1 u_1 + k_2 u_2 =0.$ Those would be the Kyle numbers. For a larger matrix, you can have similar relationships, but it gets more and more complicated. I would end up using row reduction to find the coefficients of the linear combination myself.