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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


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