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Please first take a look at http://reference.wolfram.com/language/tutorial/ExactAndApproximateResults.html Eigenvalues uses entirely different methods when working with exact or inexact quantities. mat = {{1, 1/2, 4}, {2, 1, 2}, {1/4, 1/2, 1}}; First notice that the eigenvalues are the same and returned in the same order in the two cases: ...


I believe this question is a combination of these: Annoying display truncation of numerical results Confused by (apparent) inconsistent precision A problem about function N Specifically, for your function to work as desired most directly (and correctly) it will need to return a number or expression in arbitrary precision. This is (best) done by using ...

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