       Help for Symbolic matrix manipulations in mathematica?

• To: mathgroup at smc.vnet.net
• Subject: [mg26069] Help for Symbolic matrix manipulations in mathematica?
• From: Louis Trichard <trich-lg at ee.usyd.edu.au>
• Date: Wed, 22 Nov 2000 01:55:57 -0500 (EST)
• Organization: The University of Sydney, Australia
• Sender: owner-wri-mathgroup at wolfram.com

```Hi

I'm quite new to mathematica and not sure on where to start.

What I would like to do is to initially symbolically manipulate
matrices.

i.e. find the coefficients of (R+X)^i where R and X do not
commute...ie. binomial theorem does not apply.

for example    (R+X)^2 = R^2 + RX + XR + X^2 **********1

then simplify the expression  s^t (R + X)^i s where X = s s^t and
s^t s = 1   where t indicates transpose and s is a vector.

for example **********1 will simplify to

s^t (R+X)^2 s = s^t R^2 s + s^t RX s + s^t XR s + s^t X^2 s
= s^t R^2 s + 2 s^t R s +
1                         , where s^t X = s and so forth....

of course this looks like just an application of the binomial
theorem but for i=3 we get....

s^t (R+X)^3 s = s^t R^3 s + 2 s^t R^2 s + (s^t R s)^2 + 3 s^t R s +
1....

So I would like to have a program which can give me the coefficients
etc for an arbitrary i...

Can mathematica do it, if so, could someone point me in the right
direction to do such a thing...

Thanks

Louis

```

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