I. Linear Algebra
The first part of this course is on linear algebra. We begin by introducing matrices and matrix algebra. Next, the important algorithm of Gaussian elimination and LU-decomposition is presented and used to solve a system of linear equations and invert a matrix. We then discuss the abstract concept of vector and inner product spaces, and show how these concepts are related to matrices. Finally, a thorough presentation of determinants is given and the determinant is then used to solve the very important eigenvalue problem.
Thumbnail: 3 planes intersect at a point. (CC BY-SA 4.0; Fred the Oyster).