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

```

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