Linear Algebra and Discrete Mathematics
Course Syllabus
| Course Code: | Α1Υ |
| Semester: | 1st |
| ECTS units: | 5 |
| Weekly Teaching Hours: | 5 |
| Course Page: | https://eclass.duth.gr/courses/TME244/ |
| Instructors: | SPARTALIS STEPHANOS |
Course Description
Systems of linear equations. The n-dimensional Euclidean space. Algebra of matrices. Determinants. Scalar and invertible matrices, applications. Vector spaces, subspaces, basis, dimension. Elementary matrix transformations. Eigenvalues and Eigenvectors. Characteristic matrix equation. Diagonalization. Similar matrices, quadratic forms. Linear representations. Combinatorics, theory of transpositions and graphs, trees, monoids.
Purpose of the course
Introduce students to a comprehensive view of the properties and basic rules of behavior of the mathematical object of the mn matrix as a tool for transferring large-flow encoded information. Familiarization with the applications of matrices in solving linear systems, in optimization algorithms (simplex, etc.), in robotics – kinematics (transfer and rotation matrices). Training of students in the calculation of derivatives and integrals using the matrix method.
