Re: Simplifying {0,0,0}.X.{0,0,0}

• To: mathgroup at smc.vnet.net
• Subject: [mg74031] Re: Simplifying {0,0,0}.X.{0,0,0}
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Wed, 7 Mar 2007 03:07:04 -0500 (EST)
• References: <esjg5a\$26q\$1@smc.vnet.net>

Hi,

X /: Dot[X, a : {0 ..}] := a

will help.

Regards
Jens

Will Robertson wrote:
> Hello,
>
> In brief: Is there a way that I can specify that "X" is a matrix and
> will resolve to zero when dot multiplied with a vector of zeros?
>
> I'm constructing a swathe of expressions that contain things like
> (when expanded): {0,0,0}.X.{0,0,0}, where X is an arbitrary (well,
> positive definite) square matrix of obvious size, and I'd like to be
> able to have mathematica simplify that for me without much
> intervention.
>
> My only option at the moment is to manually perform the replacements
> {{0, 0, 0}.X._ -> 0, _.X.{0, 0, 0} -> 0} (the left and right vectors
> won't always both be zeros), but this is tedious to perform for a
> large number of expressions. I could also define the matrix X in terms
> of its indices and end up with expressions in terms of x11, x12, ... ,
> x33, but I'd rather not do that.
>
> Any help would be greatly appreciated.
>