This conceptual history of the theory of matrices as of the 1930s provides an example of how mathematics becomes internationalized: from various scattered, isolated strands, a standard notation and vocabulary evolves into a “universal” mathematical language. The author identifies a network of connections of mathematicians in the eighteenth and nineteenth centuries. A modern history of the status of matrices, beginning with Arthur Cayley early in the nineteenth century, is given. Various further strands were developed in the twentieth century as reflected especially in the papers and books created between the two world wars within centers located in the United Sates (especially Chicago) and Europe. The results of various tabulations (relying on the Zentralblatt database) are given graphically as appendices, along with reproductions of several pages from [{\it A. Aitken} and {\it H. Turnbull}, An Introduction to the Theory of Canonical Matrices. London, Glasgow and Bombay; Blackie \& Son (1932; JFM 58.0101.01)].

Reviewer:

Albert C. Lewis (Austin)