2015-08-11 , Nagoya University OpenCourseWare Steering Committee
Linearity is one of the most basic concepts for handling quantities in current natural sciences. Indispensable in quantum mechanics and relativity, its use has spread across all branches of natural sciences and beyond. Linear algebra, developed in the Nineteenth century, is the mathematical theory of linearity. The first half of this one-year course focuses on the techniques for manipulating systems of linear equations and their application to analytic geometry (in arbitrary dimensions). The second half focuses on a deeper study of linear maps (composition, invertibility, eigenvectors and eigenvalues...). The notions of scalar product and determinant will also be studied, and the semester will end with an introduction to complex numbers.