My talk is concerned with the history of two theorems set during the 1860ies in the background of two different traditions (Weierstrass 1868, Jordan 1870). My research therefore lies on the history of linear algebra in the 19th century. I will argue there is much more in the history of the Jordan normal form than linear algebra. It is also about forms in mathematics. I will display my researches on representations in mathematics and representations of mathematics in the 19th century

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