Linear Algebra

 Title ΓΡΑΜΜΙΚΗ ΑΛΓΕΒΡΑ / Linear Algebra Code 0108Α Faculty Sciences School Mathematics Cycle / Level 1st / Undergraduate Teaching Period Winter/Spring Common Yes Status Active Course ID 600019627

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

Registered students: 588
OrientationAttendance TypeSemesterYearECTS
CoreCompulsory Course216.5

 Academic Year 2020 – 2021 Class Period Spring Faculty Instructors Athanasios Papistas 65hrs Instructors from Other Categories Charilaos Vavatsoulas 91hrs Weekly Hours 6 Class ID 600166748
SectionInstructors
1. ΤΜΗΜΑ ΑAthanasios Papistas, Charilaos Vavatsoulas
2. ΤΜΗΜΑ ΒCharilaos Vavatsoulas
3. ΦΡΟΝΤΙΣΤΗΡΙΟCharilaos Vavatsoulas
4. ΕΡΓΑΣΤΗΡΙΟCharilaos Vavatsoulas
Type of the Course
• Scientific Area
• Skills Development
Course Category
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
• 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.
Keywords
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
Lectures652.2
Laboratory Work130.4
Tutorial260.9
Exams30.1
Total2408
Student Assessment
Description
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)
Bibliography
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
Last Update
30-11-2020