Re: limits on symbol eigenvalues?
- To: mathgroup at smc.vnet.net
- Subject: [mg132717] Re: limits on symbol eigenvalues?
- From: David Bailey <dave at removedbailey.co.uk>
- Date: Mon, 12 May 2014 00:44:03 -0400 (EDT)
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On 04/06/2004 10:14, Uwe Brauer wrote: > Hello > > I just started using mathematica. When I tried to calculate the > symbolic eigenvalues of a 16x16 matrix mathematica told me it couldn't > > Is there a restriction? > > Thanks > > Uwe Brauer > Not every symbolic problem that you can pose has a symbolic solution. For example, some symbolic integrals don't have symbolic solutions - likewise for differential equations. A symbolic eigenvalue problem of order N involves solving an N'th order polynomial equation. Specific cases can be solved, but the general case cannot be solved for N>=5. This restriction can in theory be relaxed (I am not sure by how much) by the use of theta functions, though the symbolic answers are impossibly large. Even when a symbolic solution is possible, it may not be desirable because it is excessively complicated, and possibly numerically unstable if the coefficients are subsequently replaced by numbers. To see what I mean, try evaluating: Solve[a x^4 + b x^3 + c x + d == 0, x] David Bailey http://www.dbaileyconsultancy.co.uk