Cracovians: The Twisted Twins of Matrices

Linear algebra is typically explained using matrices. But matrix theory is just one possible perspective. Below, I describe an alternative approach to linear algebra. Tadeusz Banachiewicz (1882–1954), a Polish astronomer living in Krakow, was passionate about calculating machines. From the 1920s, Banachiewicz developed a method for computations on tables of numbers, which was particularly easy [ ]