[Haskell-cafe] matrix computations based on the GSL

Dan Piponi dpiponi at mac.com
Wed Jun 29 13:39:47 EDT 2005

>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*.

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