On Tue, Sep 16, 2008 at 3:09 PM, John Randall <[EMAIL PROTECTED]> wrote: > Representations of linear maps come from choosing bases, thereby > giving coordinates. If we do that, it's reasonably straightforward > except that we are misled by the 1-dimensional case.
The wikipedia page on linear maps expresses some qualities of linear maps in terms of addition and multiplication. This implies, to me, that in the context of any linear map, there must be some value that corresponds to 0, and some other value which corresponds to 1. (If this is not the case, then there must be some way of defining addition and multiplication which does not conform to the peano postulates?) That wikipedia page also asserts: Differentiation is a linear map from the space of all differentiable functions to the space of all functions. I think I can use the constant zero function for 0, but I am having a problem figuring out what 1 would be. Does anyone know? (By constant zero function, I mean J's 0: more or less -- there might be an issue with J rank which corresponds roughly to the space over which the differentiable functions are defined? I suspect that that wikipedia assertion about differentiation should be constrained to functions over a given space, since I can not see how to support linear combinations of functions which were defined over arbitrarily different spaces.) Thanks, -- Raul ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
