Simplifying {0,0,0}.X.{0,0,0}

*To*: mathgroup at smc.vnet.net*Subject*: [mg74022] Simplifying {0,0,0}.X.{0,0,0}*From*: "Will Robertson" <wspr81 at gmail.com>*Date*: Tue, 6 Mar 2007 05:31:28 -0500 (EST)

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