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I have to diagonalise this HUGE $9\times 9$ matrix with symbolic entries which are made up of three independent variables.

Can you please give me a reference as to how to do such a thing numerically? an algorithm or such would be nice!

the matrix i am trying to work on is here. Take a look if it helps.

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This will never render properly. It's too large to include in the question. –  Alex Becker Apr 19 '12 at 7:33
which is why i removed it. But if you take a look and find some pattern that perhaps relegates it to a solvable class of matrices - please do!@alex –  Debanjan Basu Apr 19 '12 at 7:40
If the matrix is Hermitian, things are slightly nice. Otherwise... –  J. M. Apr 19 '12 at 7:40
I checked a few entries - i suppose it is symmetric - hence hermitian. Is there an answer? –  Debanjan Basu Apr 19 '12 at 7:46
Maybe you should use some abbreviations for e.g. ${\left(\frac{1}{\alpha_{1}} + \frac{1}{\alpha_{2}} + \frac{1}{\alpha_{3}}\right)}$ to get an better overview! –  draks ... Apr 19 '12 at 8:52

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