Linear Algebra

Course Information
TitleΓΡΑΜΜΙΚΗ ΑΛΓΕΒΡΑ / Linear Algebra
Cycle / Level1st / Undergraduate
Teaching PeriodWinter/Spring
Course ID600019627

Programme of Study: UPS of School of Mathematics (2014-today)

Registered students: 588
OrientationAttendance TypeSemesterYearECTS
CoreCompulsory Course216.5

Class Information
Academic Year2020 – 2021
Class PeriodSpring
Faculty Instructors
Instructors from Other Categories
Weekly Hours6
Class ID
1. ΤΜΗΜΑ ΑAthanasios Papistas, Charilaos Vavatsoulas
2. ΤΜΗΜΑ ΒCharilaos Vavatsoulas
3. ΦΡΟΝΤΙΣΤΗΡΙΟCharilaos Vavatsoulas
4. ΕΡΓΑΣΤΗΡΙΟCharilaos Vavatsoulas
Course Type 2016-2020
  • Scientific Area
  • Skills Development
Course Type 2011-2015
Specific Foundation / Core
Mode of Delivery
  • Face to face
Language of Instruction
  • Greek (Instruction, Examination)
Learning Outcomes
Upon successful completion of the course the students will be able to i) use matrices as tools for theoretical and arithmetical calculations ii) to compute rank of a matrix iii) to compute determinants iv) to solve systems of linear equations v) to understand and use notions of vector spaces vi) to compute eigenvalues and eigenvectors vii) to diagonalize matrices viii) to compute orthonormal bases and orthonormal projections to subspaces ix) to diagonalize symmetric matrices with the use of orthogonal matrices x) to calculate the minimal polynomial of an endomorphism and a matrix
General Competences
  • Apply knowledge in practice
  • Retrieve, analyse and synthesise data and information, with the use of necessary technologies
  • Adapt to new situations
  • Make decisions
  • Work autonomously
  • Appreciate diversity and multiculturality
  • Be critical and self-critical
  • Advance free, creative and causative thinking
Course Content (Syllabus)
Vector spaces, Vector subspaces, Linear dependence, Linear independence, Basis, Dimension, Linear mappings, The matrix representation of a linear map, System of linear equations, Eigenvalues, Quotient space, Dual space, Eigenvectors, Eigenspaces, Diagonalizable endomorphism and matrix, Minimal polynomial, The Cayley-Hamilton Theorem, Inner product spaces, The Gram-Schmidt orthogonalization process, Orthogonal complement, The Adjoint of an endomorphism, Quadratic forms.
vector spaces
Educational Material Types
  • Notes
  • Video lectures
  • Book
Use of Information and Communication Technologies
Use of ICT
  • Use of ICT in Course Teaching
  • Use of ICT in Laboratory Teaching
  • Use of ICT in Communication with Students
  • Use of ICT in Student Assessment
Course Organization
Laboratory Work130.4
Reading Assigment1334.4
Student Assessment
Written examination. Lab.
Student Assessment methods
  • Written Exam with Short Answer Questions (Formative, Summative)
  • Written Exam with Extended Answer Questions (Formative)
  • Written Exam with Problem Solving (Formative, Summative)
  • Labortatory Assignment (Formative)
Course Bibliography (Eudoxus)
1.Γραμμική Άλγεβρα, Θ. Θεοχάρη-Αποστολίδη, Χ. Χαραλάμπους, Χ. Βαβατσούλας, ΤΖΙΟΛΑ, 2017 2. Εισαγωγή στη Γραμμική Άλγεβρα, Αθ. Πάπιστας, ISBN: 978-960-418-841-3, Εκδόσεις Α. ΤΖΙΟΛΑ & ΥΙΟΙ Α.Ε., ID Ευδόξου: 86196159, 2019 3.Γραμμική άλγεβρα, Ε. Ψωμόπουλος, ISBN: 978-960-456-424-8, ΖΗΤΗ, 2014 4.Μία Εισαγωγή στη Γραμμική Άλγεβρα, A.O.MORRIS, ISBN: 978-960-7258-55-7, ΠΝΕΥΜΑΤΙΚΟΣ 5.Εισαγωγή στη Γραμμική Άλγεβρα, Σ. Μποζαπαλίδης, ISBN: 978-960-99293-5-6, ΑΙΒΑΖΗΣ, 2010 6.Ασκήσεις Γραμμικής Άλγεβρας, Σ. Μποζαπαλίδης, ΑΙΒΑΖΗΣ, 2010 7.Μία Εισαγωγή στη Γραμμική Άλγεβρα, Δ. Βάρσος, Δ. Δεριζιώτης, Γ. Εμμανουήλ, Μ. Μαλιάκας, Α. Μελάς, Ο. Ταλλέλη, ISBN: 978-960-6706-36-3, ΣΟΦΙΑ, 2012 8.Γραμμική Άλγεβρα και Εφαρμογές, S. Gilbert, ISBN: 978-960-524-7309-70-9, Πανεπιστημιακές Εκδόσεις Κρήτης 9. Μία Εισαγωγή στη Γραμμική Άλγεβρα, Χ. Χαραλάμπους, Α. Φωτιάδης, ISBN: 978-960-603-273-8, [ηλεκτρ. βιβλ.] Αθήνα:Σύνδεσμος Ελληνικών Ακαδημαϊκών Βιβλιοθηκών, ID Ευδόξου: 320185
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