Re: Help with Root function
- To: mathgroup at smc.vnet.net
- Subject: [mg79470] Re: Help with Root function
- From: David Bailey <dave at Remove_Thisdbailey.co.uk>
- Date: Fri, 27 Jul 2007 05:57:28 -0400 (EDT)
- References: <f89q55$5nu$1@smc.vnet.net>
jeremito wrote:
> I am trying to find the eigenvalues of a 3x3 matrix with non-numeric
> elements. This requires finding the roots of cubic polynomials.
> Mathematica can do this, but I know how to interpret its output. For
> example
>
> In[1]:= B = {{a, 1, 1}, {1, b, 1}, {1, 1, c}}
>
> Out[1]= {{a, 1, 1}, {1, b, 1}, {1, 1, c}}
>
> In[2]:= Eigenvalues[B]
>
> Out[2]= {Root[-2 + a + b + c -
> a b c + (-3 + a b + a c + b c) #1 + (-a - b - c) #1^2 + #1^3 &,
> 1], Root[-2 + a + b + c -
> a b c + (-3 + a b + a c + b c) #1 + (-a - b - c) #1^2 + #1^3 &,
> 2], Root[-2 + a + b + c -
> a b c + (-3 + a b + a c + b c) #1 + (-a - b - c) #1^2 + #1^3 &,
> 3]}
>
>
> How can I get Mathematica to give me the full answer? I know it is
> long and ugly, but at least I can do something with it. I can't do
> anything with what it gives me now. Does that make sense?
> Thanks,
> Jeremy
>
>
You can set the options Cubics->True and Quartics->True on Eigenvalues
to get the explicit symbolic solutions, but as you say, these are not
pretty, and inevitably involve complex numbers. If possible, I would
delay calculating the eigenvalues until you have numerical values for
the variables.
David Bailey
http://www.dbaileyconsultancy.co.uk