Re: Mathematica question about commutativity of multiplication

• To: mathgroup at smc.vnet.net
• Subject: [mg96718] Re: Mathematica question about commutativity of multiplication
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Sun, 22 Feb 2009 03:11:33 -0500 (EST)
• References: <gnq6u3\$89g\$1@smc.vnet.net>

```Hi,

what had you expect, a 6 x 6 matrix have a 6. order
characteristic polynomial. A closed form for 6. order
polynomials does not exist and inserting all roots
of the characteristic polynomial in to the matrix
will make the expression not simpler.

The question
"I think part of the issue is that
> in my case, the variables a,b, and c commute. "

is a bit unclear, Mathematica will always assume that
a*b==b*a and the only way to have multiplication that
does not commute is to use not Times[] but NonCommutativeMultiply[].

#1 is the short form of Slot[1] and #1^5 means the 5. power
of Slot[1] as well as a^5 means the 5. power of a.
And a^5 means a*a*a*a*a

Regards
Jens

James wrote:
> 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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