Linear Algebra

This course introduces students to the fundamental concepts and methods of Linear Algebra, essential for their theoretical and practical foundation in Computer Science. Topics include systems of linear equations, matrices, determinants, vector spaces, linear mappings, eigenvalues, eigenvectors, and matrix diagonalization. A brief introduction to set theory and algebraic structures is also provided.

Applications of these concepts to Computer Science are highlighted through examples, such as image processing, computer graphics, machine learning, and data analysis. The course also introduces suitable computational tools (e.g., MATLAB/Octave) and web-based applications for solving practical problems.

Upon successful completion of the course, students will be able to:

• recognize algebraic structures
• perform matrix operations
• calculate determinants
• solve linear systems using Gauss method, Gauss-Jordan method, Cramer’s rule, and the inverse matrix method
• recognize vector spaces and subspaces
• test for linear dependence of vectors
• find a base and the dimension of a vector space
• calculate inner products and norms of vetors
• find the kernel and the image of a linear map
• calculate the eigenvalues and eigenvectors of a matrix
• diagonalize a matrix

Sets – Cartesian Products – Relations – Operations – Algebraic Structures – Matrices and Matrix Operations – Linear Systems – Gauss Method – Gauss-Jordan Method – Calculation of the Inverse of a Matrix – Determinants and their Properties – The Cramer’s Rule – Vector Spaces – Subspaces – Linear Independence –Base and Dimension – Inner Product Spaces – Linear Maps – Kernel and Image – Eigenvalues and Eigenvectors of a Matrix – Matrix Diagonalization

• Varsos, D., Deriziotis, D., Emmanouil, I., Maliakas, M., Melas, A., Talelli, O., An Introduction to Linear Algebra, Sofia Publications, 2012, ISBN: 978-960-6706-36-3.
• Donatos, G. S., Adam, M. Ch., Linear Algebra, Gutenberg Publications, 2008, ISBN: 978-960-01-1193-4.

• Lectures
• Tutorial exercises
• Student participation in tutorials

• Support of the educational process via the e-learning platform Opencourses
• Use of ICT in teaching and education (specialized software, electronic lecture notes)
• Use of ICT for communication with students

Written final examination with problem-solving questions