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Re: Applying restrictions on matrix multiplication

• To: mathgroup at smc.vnet.net
• Subject: [mg13615] Re: Applying restrictions on matrix multiplication
• From: Carl Woll <carlw at fermi.phys.washington.edu>
• Date: Fri, 7 Aug 1998 03:08:17 -0400
• Organization: University of Washington
• References: <6puih4$6th@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

Hi,

One way to have Mathematica automatically set products to zero is to use
upvalues. For example, if you wanted products of expressions with the
head z to be set to zero, you could use the rule

z /: a_z b_z := 0

A slight problem in your case is that you are working with subscripts,
and so you can't associate the upvalues with E as E is too deep. So,
you will need to associate upvalues with Subscript instead, as in

Subscript /: Subscript[E,_] Subscript[E,_] := 0

Instead of the above rule, you could of course write out the rule using
2-D syntax.

Carl Woll
Dept of Physics
U of Washington

On 1 Aug 1998, Van Graves wrote:

> I need some help applying restrictions on multiplying two matrices
> within Mathematica.  The elements contain expressions of Ex, Ey, Ez
> (where E=greek letter sigma and the xyz are subscripts).  In these
> matrices, the E terms are assumed to be nearly zero, so I would like to
> throw out any terms where two or more E's are multiplied together, thus
> simplifying the resultant matrix before applying it with another one
> (these are transformation matrices).
> 
> If T01 and T12 are two 4x4 matrices, can I somehow place a restriction
> on T01.T12 to get a simplified result?  Or can I simplify the result
> after it's calculated?
> 
> Thanks for any help.
> 
> ***********
> Van Graves
> Oak Ridge National Laboratory          gravesvb at ornl.gov University of
> Tennessee                vgraves at utk.edu ***********
> 
> 
>