Linear Algebra (1ΚΠ02)
Instructor : Maria Adam
Course typeCompulsory
Semester1
TermFall Semester
ECTS5
Teaching hours3
Laboratory hours1
Description
• Matrix algebra-basic properties. Invertible matrices and their properties. • Determinants and their properties. Computing the inverse of a matrix. • Matrices and systems of linear equations. Rank of a matrix. Solving linear systems-Algorithms Gauss and Cramer. • Vector spaces and subspaces. Special vector subspaces (sum, intersection, orthogonal complement). Linear combinations, linear dependence-independence of vectors. Basis and dimension of a vector space. • Linear transformation – Kernel and Image of a linear transformation. Rank–nullity theorem. Matrix of a linear transformation. Similar matrices. • Inner product on a vector space. Norm of a vector. Orthonormalization of a basis. Gram-Schmidt algorithm. Orthogonal spaces and basic theorems. • Properties of eigenvalues and eingenvectors of a matrix. Theorem Cayley- Hamilton. Minimal polynomial. • Canonical forms. Diagonalizing of a matrix. Criteria diagonalizable matrix (linear transformation). Spectral theorem. Applications. • Quadratic forms-basic criteria for symmetric matrices. Applications to quadratic forms on the problems min-max of a function of several real variables.
Course objectives

Since the topic of the course is the study of fundamental concepts of the linear algebra such as vector spaces and linear transformation, the matrix theory is an essential tool in the study and modeling of many mathematical problems and the concept of the matrix is unfamiliar to the student, the main aim of the course is:

  • to familiarize students with the concept of the matrix, to present the basic methods of solving linear systems, to study the basic and characteristic properties of the square matrices,
  • the development of computational methods and techniques for the calculation of various sizes, and
  • the theoretical study of properties of topics, such as vector spaces.

The course aims at the acquisition of knowledge and skills so that they can be applied to other courses of mathematics and computer science.

Textbooks/Bibliography
  • Δονάτος Γ., Αδάμ Μ., Γραμμική Άλγεβρα-Θεωρία και Εφαρμογές, Γ. Δαρδανός,  Κ. Δαρδανός Ο.Ε., έκδοση 1η, 2008, Αθήνα.
  • Στεφανίδης Γ., Γραμμική Άλγεβρα με το Matlab: Νέα έκδοση, εκδόσεις Γ.Ι. Μάρκου & ΣΙΑ ΕΕ, έκδοση 1η, 2014, Θεσσαλονίκη.
  • Χατζάρας Ι., Γραμμένος Θ., Εισαγωγή στη Γραμμική Άλγεβρα, εκδόσεις Α. Τζιόλας & ΥΙΟΙ Α.Ε., έκδοση 1η, 2011, Θεσσαλονίκη.
  • Κυριαζής Αθ., Εφαρμοσμένη Γραμμική Άλγεβρα, εκδόσεις Ε. Νικητόπουλος & ΣΙΑ ΟΕ, έκδοση 1η, 2006, Αθήνα.
  • Gilbert Strang, Γραμμική Άλγεβρα και Εφαρμογές, Πανεπιστημιακές Εκδόσεις Κρήτης, ΙΤΕ, έκδοση 1η, 2009, Ηράκλειο Κρήτης.
  • Καδιανάκης Ν., Καρανάσιος Σ., Γραμμική Άλγεβρα Αναλυτική Γεωμετρία και Εφαρμογές,  εκδόσεις Νικ. Καδιανάκης, έκδοση 4η, 2008, Αθήνα.
  • Μυλωνάς Νίκος, Γραμμική Άλγεβρα και Αναλυτική Γεωμετρία, εκδόσεις Α. Τζιόλας & ΥΙΟΙ Α.Ε., έκδοση 1η, 2013, Θεσσαλονίκη.
Assessment method
Mandatory written exams at the end of the semester.
Course material
http://eclass.uth.gr/eclass/courses/DIB102/