Property of TransformationFunction
- To: mathgroup at smc.vnet.net
- Subject: [mg79127] Property of TransformationFunction
- From: "David Park" <djmpark at comcast.net>
- Date: Thu, 19 Jul 2007 03:32:02 -0400 (EDT)
TransformationFunction has what seems to me like a useful but strange
attribute. TransformationFunctions operate on vectors. However, if given a
list of vectors, that is a matrix, then it will operate on the individual
vectors in the list. It is a little like being Listable but only for lists
of vectors. I wondered if there are any other functions that behave in this
manner?
Although the documentation does not seem to explicity describe this
behavior, it is illustrated in the documentation for ReflectionTransform
under Scope.
rt = ReflectionTransform[{u, v, w}] //
Simplify[#, {{u, v, w} \[Element] Reals, u^2 + v^2 + w^2 == 1}] &
givining a TransformationFunction.
Normally it would operate on a vector such as
rt@{x, y, z}
But the documentation has it operating on a list of vectors: (Showing that
vectors in the reflection plane are unchanged)
NullSpace[{{u, v, w}}]
rt@% // Simplify
--
David Park
djmpark at comcast.net
http://home.comcast.net/~djmpark/