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Re: How to simplify transposed terms?
*To*: mathgroup at smc.vnet.net
*Subject*: [mg2720] Re: How to simplify transposed terms?
*From*: rubin at msu.edu (Paul A. Rubin)
*Date*: Sat, 9 Dec 1995 01:55:47 -0500
*Organization*: Michigan State University
In article <49do0r$8a6 at dragonfly.wri.com>,
Bernd.Cebulski at e-technik.tu-chemnitz.de (Bernd Cebulski) wrote:
->How could I tell MMA to simplify
->
->Transpose[A*B] ---> Transpose[B]*Transpose[A]
->Transpose[A+B] ---> Transpose[A]+Transpose[B]
->
->And how could I declare 'A' as a matrix without giving values to it, so
that
->calculations like the 2 examples could be made. Of course they should be
a
->little more complicated ...
->
->Tnx,
->
-> Bernd.
->
-> -----------------------------------------------.
->| Chemnitz, University of Technology |
->|--- bernd.cebulski at e-technik.tu-chemnitz.de ---|
->| Phone: +49 (371) 5313318 |
->| Fax: +49 (371) 5313361 |
->| DL 1 DTP |
->`------------------------------------------------
First step, unprotect Transpose and add the desired properties:
Unprotect[Transpose];
Transpose[ A_ B_ ] := Transpose[ B ] Transpose[ A ] /;
MatrixQ[ A ] && MatrixQ[ B ]
Transpose[ A_ + B_ ] := Transpose[ A ] + Transpose[ B ] /;
MatrixQ[ A ] && MatrixQ[ B ]
Protect[ Transpose ];
Note that I've restricted the properties to apply only when both arguments
are recognizable as matrices. (You could also do this with the alternate
notation
Transpose[ A_?MatrixQ B_?MatrixQ ] := Transpose[ A ] Transpose[ B ]
and similarly for distribution across addition.)
The next step is to define symbols to be matrices using up-values. Note
that for undefined A and B, the properties are not invoked:
In[]:= Transpose[ A B ]
Out[]= Transpose[A*B]
In[]:= Transpose[ A + B ]
Out[]= Transpose[A + B]
But if we define A and B to be matrices then the properties are applied:
In[]:= A /: MatrixQ[ A ] := True
In[]:= B /: MatrixQ[ B ] := True
In[]:= Transpose[ A B ]
Out[]= Transpose[A]*Transpose[B]
In[]:= Transpose[ A + B ]
Out[]= Transpose[A] + Transpose[B]
Hope this helps.
Paul
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* Paul A. Rubin Phone: (517) 432-3509 *
* Department of Management Fax: (517) 432-1111 *
* Eli Broad Graduate School of Management Net: RUBIN at MSU.EDU *
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