Linear algebra appears as a fundamental language in natural sciences in an essential way. Linear algebra also provides the first step toward understanding and manipulating abstract algebraic systems. The two-semester course covers basic concepts of linear algebra needed for students in mathematics department. Explicit goals in the first semester include familiarizing students with linear spaces (possibly equipped with additional structures), linear transformations and their matrix representatives, kernels, quotients, dual spaces, eigenvalues, and etc..
The basic materials in the second semester include the structure theorem of linear endomorphisms (the Jordan and rational canonical forms) and the study of spaces with product structure and their applications. Additional topics may include an introduction to multilinear algebra or to linear groups.