History of Jordan's Matrix Decomposition Theorem (1870-1930)

The document examined the historical development and controversies surrounding the Jordan decomposition theorem from 1870 to 1930, focusing on the debates between Camille Jordan and Leopold Kronecker. The controversy revolved around their differing approaches to algebraic reduction, with Jordan emphasizing simplicity and canonical forms, while Kronecker favored practical arithmetic methods. The document highlighted the contributions of other mathematicians like Weierstrass and Frobenius, who played roles in reconciling these approaches. The study provided insights into the evolution of linear algebra, the cultural and epistemological implications of these debates, and the eventual recognition of Jordan's work as foundational in the field.