Re: making a function linear
- To: mathgroup at smc.vnet.net
- Subject: [mg25491] Re: [mg25473] making a function linear
- From: Ken Levasseur <Kenneth_Levasseur at uml.edu>
- Date: Thu, 5 Oct 2000 23:50:12 -0400 (EDT)
- Organization: UMass Lowell
- References: <200010030226.WAA06503@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Murray: The only approach I can think of uses Hold. I understand what you mean about tring to avoid using some variation of Hold, but in a way that mirrors some of the problems I've had teaching students linear algebra. The impulse is to look at cx+y as a single vector to be mapped by T. You want them to look at it as a pattern or form; so maybe Hold is really natural. Ken Levasseur UMass Lowell Murray Eisenberg wrote: > > For a function T not yet having any "definition by formula" (T[x_] := > ..... ), I want to specify the linearity rules: > > T[x_?VectorQ + y_?VectorQ] := T[x] + T[y] > > T[c_ x_?VectorQ] := c T[x] > > Then, merely by specifying, say, > > a = {1, 2}; T[a] = {3, 4}; > b = {5, 6}; T[b] = {7, 8}; > > evaluating > > T[2 a] > T[a + b] > > would return results: > > {6, 8} > {10, 12} > > The trouble is, of course, that Mathematica first evaluates 2 a and a + > b when a and b have actual numeric values, so the two linearity rules > never get used. > > What is a SIMPLE way (if there is one) to accomplish this -- preferably > some way to do it that does not explicitly require using some Hold > variant? (I need to be able to explain how to do it early in a linear > algebra course where Mathematica is being introduced, and Hold, etc., I > consider a definitely advanced topic.) > > -- > Murray Eisenberg murray at math.umass.edu > Mathematics & Statistics Dept. phone 413 549-1020 (H) > Univ. of Massachusetts 413 545-2859 (W) > Amherst, MA 01003-4515
- References:
- making a function linear
- From: Murray Eisenberg <murray@math.umass.edu>
- making a function linear