Linear Algebra I (MAY121)

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School School of Science
Academic Unit Department of Mathematics
Level of Studies Undergraduate
Course Code MAY121
Semester 1
Course Title Linear Algebra I
Independent Teaching Activities Lectures (Weekly Teaching Hours: 5, Credits: 7.5)
Course Type General Background
Prerequisite Courses -
Language of Instruction and Examinations Greek
Is the Course Offered to Erasmus Students Yes (in English)
Course Website (URL) See eCourse, the Learning Management System maintained by the University of Ioannina.

Learning Outcomes

Learning outcomes

After finishing the course, the students will be able:

  • to use matrices as a tool in theoretical or numerical computations
  • to compute the rank of a matrix
  • to compute determinants
  • to solve linear systems of equations
  • to understand and use the notion of vector space.
General Competences The aim of the course is to empower the graduate to analyse and compose basic notions and knowledge of Linear Algebra and advance his creative and productive thinking.


  • The algebra of (m x n) matrices and applications.
  • Row echelon forms and reduced row echelon form of a matrix.
  • Rank of a matrix. Determinants. Invertible matrices.
  • Linear systems and applications.
  • Vector spaces. Linear maps.
  • The space L(E,F) of linear operations.
  • Subspaces. Bases. Dimension. Rank of a linear operation.
  • Fundamental equation of dimension and its applications. Matrix of a linear map. Matrix of a change of bases. The isomorphism between linear mapsand matrices. Equivalent matrices. Similar matrices. Determinant of an endomorphism. Sum and direct sum of vector subspaces.

Teaching and Learning Methods - Evaluation

Delivery Classroom (face-to-face)
Use of Information and Communications Technology
  • Teaching Material: Teaching material in electronic form available at the home page of the course.
  • Communication with the students:
  1. Office hours for the students (questions and problem solving).
  2. Email correspondence
  3. Weekly updates of the homepage of the course.
Teaching Methods
Activity Semester Workload
Lectures (13x5) 65
Working independently 100
Exercises-Homeworks 22.5
Course total 187.5
Student Performance Evaluation Final written exam in Greek (in case of Erasmus students, in English) which includes analysis of theoretical topics and resolving application problems.

Attached Bibliography

See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:

  • Introduction to Linear Algebra (Greek), Bozapalidis Symeon, ISBN: 978-960-99293-5-6 (Editor): Charalambos Nik. Aivazis