Approximate values of eigenvalues

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For creating random matrices, you should have a look at http://doc.sagemath.org/html/en/refer...

For computing eigenvalues, you should have a look at: http://doc.sagemath.org/html/en/const...

To work with floating-point real numbers, you should search for "real double field".

Please do not hesitate to ask for more (by providing concrete examples) if there is something unclear.