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    $\begingroup$ This sounds interesting. Can you give a reference? $\endgroup$ Commented Dec 29, 2009 at 15:57
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    $\begingroup$ or elaborate on this? $\endgroup$ Commented Dec 29, 2009 at 19:13
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    $\begingroup$ I explained the connection between CRT and Lagrange interpolation on my old blog once: artofproblemsolving.com/Forum/weblog_entry.php?t=237669 . $\endgroup$ Commented Dec 29, 2009 at 23:07
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    $\begingroup$ That's the page I was going to link! The other thing about the JNF is standard and can be found in any algebra book, but there's an exercise in Lang's Algebra in the chapter "Representations of one endomorphism" detailing the proof of the Jordan-Chevalley decomposition of an endomorphism of a vector space over an algebraically closed field. $\endgroup$ Commented Dec 29, 2009 at 23:18
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    $\begingroup$ Why is this comment on my answer rather than the op? $\endgroup$ Commented Dec 30, 2009 at 15:10