
Γραμμική Άλγεβρα
 Title:  Γραμμική Άλγεβρα  Lesson Code:  3213154  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, adjointinverse, Cramer’s rule. Characteristic polynomial, CayleyHamilton theorem, eigenvalueseigenvectors (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 nontrivial determinants should be discussed. Students must also understand more advanced topics of linear algebra, such as eigenvalueseigenvectors, 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  Presentation of the theory through examples, solutions of exercises in the teaching hours and in the problem session hours.   Assessment/Grading Methods  Final written exam.   Language of Instruction  Greek, English (for Erasmus students)   Μode of delivery  Facetoface. 

