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Linear Algebra

 Title: Linear Algebra Lesson Code: 321-3154 Semester: 2 ECTS: 5 Theory Hours: 3 Lab Hours: 2 Faculty: Kofinas Georgios

Content outline
Complex numbers, conjugate, absolute value, Argand diagram, Euler relation, De Moivre theorem, powers, roots, factorization of a polynomial. Vector spaces, subspaces, sum of subspaces, subspace generated by a set of vectors, linear independence, basis, dimension. Matrices, operations, inverse, transpose, composite matrices, row space, rank, row echelon form, triangular, symmetric, hermitian, orthogonal matrices, trace, similar matrices, row equivalence, change of basis, linear systems. Determinants, properties, Laplace expansion formula, determinant of a triangular matrix, adjoint-inverse, Cramer’s rule. Characteristic polynomial, Cayley-Hamilton theorem, eigenvalues-eigenvectors (properties for symmetric, orthogonal matrices), functions of matrices. Linear mappings, kernel, image, matrix associated with a linear map, rotations, change of basis of a linear map. Diagonalization of a matrix, functions of diagonalizable matrices, diagonalization of a hermitian matrix, quadratic forms.

Learning outcomes
The purpose of the course is to introduce the first year students to the concepts of linear algebra which usually have not been met before. After an introduction to the complex numbers, one main objective of the course is to provide a complete and working knowledge of the theory of linear spaces. The notions of linear independence, linear superposition, basis and dimension should be well understood. Another goal is the study of the theory of matrices, of row equivalence and of the solution of a linear system of equations. Techniques for computing trivial and non-trivial determinants should be discussed. Students must also understand more advanced topics of linear algebra, such as eigenvalues-eigenvectors, linear mappings and diagonalization.

Prerequisites
Not required.

Basic Textbooks
1. Linear Algebra and its Applications, Strang Gilbert, Crete University Press.
2. Instructor’s notes.

Additional References
1. Linear Algebra, S. Lang, Springer.
2. Linear Algebra, S. Andreadakis, Symmetria Eds.
3. Linear Algebra and Applications, Vol A, E. Flytzanis, Smbilios Eds.
4. Linear Algebra, Theory and Applications, G. Donatou and M. Adam, Gutenberg Eds.

Learning Activities and Teaching Methods
Homeworks, tests, final written exam.

Assessment/Grading Methods

Systematic development and explanation of the theory (and through examples), methods of solutions of exercises, solutions of exercises in the teaching hours and in the problem session hours, final written exam.

Activity Semester workload
Lectures 39 hours
Review-Problem Session
26 hours
Personal study 57 hours

Final exams 3 hours
Course total 125 hours (5 ECTS)

Language of Instruction
Greek, English (for Erasmus students)

Μode of delivery
Face-to-face.

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