Chapter 2: From Morphisms to Matrices

The “New Math” was an attempt to implant the spirit of Bourbaki in the classroom. In linear algebra this meant introducing coordinate-free linear mappings. However, all concrete examples involved matrices in low dimensions with few convincing applications. Forced by the dissonance between the students’ expectations and his own, the author finally designed a course in matrix algebra, whose beginning and end are sketched in this article. The last section gives an elementary proof of an old theorem of Camille Jordan.