Eugène Rouché (born 18 August 1832 at Sommières, Hérault, France, died the 19 August 1910 at Lunel, Hérault) was a French mathematician.
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He was an alumnus of the École Polytechnique, graduating in 1852. He went on to become professor of mathematics at the Charlemagne lyceum at the École Centrale, and admissions examiner at his alma mater. He is most well known for Rouché's theorem in complex analysis, which he published in his alma mater's institutional journal in 1862, and for the Rouché-Capelli theorem in linear algebra.