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Mathematica question about commutativity of multiplication

  • To: mathgroup at smc.vnet.net
  • Subject: [mg96708] Mathematica question about commutativity of multiplication
  • From: James <james545 at gmail.com>
  • Date: Sat, 21 Feb 2009 19:40:39 -0500 (EST)

Dear users,

I have a 6x6 matrix in terms of 
3 variables a,b,c.  That is, each entry in the matrix
is some polynomial in the variables a,b,c 
with integer coefficients.

I wish to calculate the eigenvalues of this matrix, so
if the matrix is called A, I type in Eigenvalues[A].

The problem is that the output is 500 pages long, so is
not useful to me.  I think part of the issue is that 
in my case, the variables a,b, and c commute.  That is,
ab = ba, ac = ca, and bc = cb.  I really believe that
if I could tell Mathematica that multiplication commutes
with my variables, then the output would be simpler.

My questions are : 

1) How do I let Mathematica know that multiplication with
my variables is commutative?
2) Also, when I typed Eigenvalues[A], the output had
terms such as 2ab^2 #1^5.  What is #1^5?  Is this some
sort of error?  Did I make an error somewhere?  The
output also had the symbol &.  Why is that there in
the expression of an eigenvalue?
3) I understand that with 3 variables, the eigenvalues
of a 6x6 matrix are difficult for Mathematica to compute,
so it did take 15 seconds or so...is this part of 
my problem?

Thanks so much for your help,

James


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