Re: Help with Root function
- To: mathgroup at smc.vnet.net
- Subject: [mg79439] Re: Help with Root function
- From: jeremito <jeremit0 at gmail.com>
- Date: Fri, 27 Jul 2007 05:41:13 -0400 (EDT)
- References: <f89q55$5nu$1@smc.vnet.net>
Thank you all who offered the solution to this problem. The answer
is:
Eigenvalues[B]//ToRadicals
How simple, if you know how to do it. My follow-up question is:
How could I (or anyone) have found that on their own? I searched in
the documentation, but couldn't find it until I knew what to search
for.
Thanks again,
Jeremy
On Jul 26, 5:39 am, jeremito <jerem... at gmail.com> 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
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- From: Murray Eisenberg <murray@math.umass.edu>
- Re: Re: Help with Root function