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MathGroup Archive 2007

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

  • To: mathgroup at
  • Subject: [mg74028] Re: Simplifying {0,0,0}.X.{0,0,0}
  • From: newsmetrohm <dh at>
  • Date: Wed, 7 Mar 2007 03:05:28 -0500 (EST)
  • References: <esjg5a$26q$>

Hi Will,

simply efine two rules for X:

X/: {0,0,0}.X=0;

X/: X.{0,0,0}=0


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.


> Many thanks in advance,

> Will Robertson



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