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Let <i>K</i> be a field and <i>A</i> a matrix with entries in <i>K.</i> It is well known that if det(<i>xI - A</i>) splits in <i>K,</i> there exists a regular matrix <i>P</i> with entries in <i>K,</i> such that <i>P</i><sup>-1</sup> <i>AP</i> is a diagonal matrix of Jordan blocks. Two problems arise that have been well treated in the literature. What should… (More)