Re: Multiplication of matrices

*To*: mathgroup at smc.vnet.net*Subject*: [mg102293] Re: Multiplication of matrices*From*: O <kakabomba at gmail.com>*Date*: Tue, 4 Aug 2009 04:28:56 -0400 (EDT)*References*: <h4rpe1$l70$1@smc.vnet.net>

On Jul 30, 2:33 am, "Qing" <Qing.Zhan... at uni.massey.ac.nz> wrote: > Hi: > > I have two 2x2 matrices , X and Y (x, y are the inverses resp.). I need to evaluate the following expression: > > Simplify[Tr[ > X.Y.x.Y.x.y.X.y.X.y.x.Y.x.Y.X.y.X.y.X.Y.x.Y.x.Y.X.y.X.y.x.Y.x.Y.x.y.X.y.X.\ > y.x.Y.x.Y.X.y.X.y.X.Y.x.Y.x.y.X.y.X.y.x.Y.x.Y.x.y.X.y.X.Y.x.Y.x.Y.X.y.X.y]] > > but for some reason, mathematica can't do it and I need to break it into the following form: > > Clear[U1, U2, U3, U3, U4, U] > U1 = Simplify[X.Y.x.Y.x.y.X.y.X.y.x.Y.x.Y.X.y.X]; > U2 = Simplify[y.X.Y.x.Y.x.Y.X.y.X.y.x.Y.x.Y.x.y.X.y]; > U3 = Simplify[X.y.x.Y.x.Y.X.y.X.y.X.Y.x.Y.x.y.X.y.X.y.x]; > U4 = Simplify[Y.x.Y.x.y.X.y.X.Y.x.Y.x.Y.X.y.X.y]; > U = Simplify[U1.U2.U3.U4]; > Simplify[Tr[U]] > > I have hundreds of such expression to evaluate, it is time-consuming if I break every expression by hand. Is there anyone who knows how to write a function to do this sort of task? > > Hopefully you understand my question. > > Thanks a lot. > > Qing there are nay rule in dividing product into four parts? there any rule in full sequence X.Y.x.Y.x.y.X.y.X.y.x.Y.x.Y.X.y.X.y.X.Y.x.Y.x.Y.X.y.X.y.x.Y.x.Y.x.y.X.y.X. \ y.x.Y.x.Y.X.y.X.y.X.Y.x.Y.x.y.X.y.X.y.x.Y.x.Y.x.y.X.y.X.Y.x.Y.x.Y.X.y.X.y O