>On Wed, 29 Jun 2005, Jacques Carette wrote:
>Distinction of row and column vectors is a misconcept
Row and column vectors are sometimes worth distinguishing because they can
represent entirely different types of object. For example, if a column vector
represents an element of a vector space V over a field F, then row vectors can
be used to represent elements of the dual space, V* = {f:V->F, f linear}. Quite
different objects and in some applications it makes sense to distinguish them.
>You would never try to transpose a function.
Funny you say that, that's exactly what I've been writing Haskell code to do,
at least for linear functions. Given any linear function f:V->W then the dual
function, written f* maps W*->V*. In effect this is the transpose and it makes
perfect sense.
> So what is the operation of transposition? A type conversion?
It maps objects of type V to objects of type V* and objects of type V->W to
objects of type W*->V*.
--
Dan
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