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Re: limits on symbol eigenvalues?
Posted:
May 12, 2014 12:44 AM


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



