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