Although it is an ill-posed problem as B Kågström said in "An algorithm for numerical computation of the Jordan normal form of a complex matrix", I wonder what people do when they need to do Jordan decomposition in real life. For example, how to decompose a 1000*1000 real matrix( we may only consider the case that all eigenvalues are real).
2026-03-27 00:02:26.1774569746
Is there any algorithm (if possible, I need the codes) for Jordan normal form decomposition for large matrices in practice?
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Numerical algorithms avoid making use of the Jordan canonical form for exactly the reason you mention: the Jordan form is not continuous in the entries of the matrix. But if you're sure you need it for your application, a starting point is Beelen & Dooren 1990 and the references therein: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.29.3971&rep=rep1&type=pdf