On 12-Feb-2001 William Lee Irwin III wrote: | On Mon, Feb 12, 2001 at 02:13:38PM -0700, Joe Fasel wrote: |> signum does make sense. You want abs and signum to obey these laws: |> |> x == abs x * signum x |> abs (signum x) == (if abs x == 0 then 0 else 1) |> |> Thus, having fixed an appropriate matrix norm, signum is a normalization |> function, just as with reals and complexes. | | This works fine for matrices of reals, for matrices of integers and | polynomials over integers and the like, it breaks down quite quickly. | It's unclear that in domains like that, the norm would be meaningful | (in the sense of something we might want to compute) or that it would | have a type that meshes well with a class hierarchy we might want to | design. Matrices over Z/nZ for various n and Galois fields, and perhaps | various other unordered algebraically incomplete rings explode this | further still. Fair enough. So, the real question is not whether signum makes sense, but whether abs does. I guess the answer is that it does for matrix rings over division rings. Cheers, --Joe Joseph H. Fasel, Ph.D. email: jhf@lanl.gov Technology Modeling and Analysis phone: +1 505 667 7158 University of California fax: +1 505 667 2960 Los Alamos National Laboratory post: TSA-7 MS F609; Los Alamos, NM 87545