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Linear Algebra II (MAY221)

Linear Algebra II (MAY221)

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General

School School of Science
Academic Unit Department of Mathematics
Level of Studies Undergraduate
Course Code MAY221
Semester 2
Course Title Linear Algebra II
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) http://users.uoi.gr/abeligia/LinearAlgebraII/LAII2018/LAII2018.html

Learning Outcomes

Learning outcomes

After finishing the course, the students will be able:

  • to compute eigenvalues and eigenvectors
  • to diagonalize matrices
  • to compute othocanonical bases, orthogonal complements and orthogonal projections to subspaces
  • to diagonalise symmetric matrices using orthogonal matrices
  • to compute the invariants of quadratic forms.
General Competences

The aim of the course is to empower the graduate to analyse and compose notions and knowledge of Linear Algebra and advance creative and productive thinking.

Syllabus

Eigenvalues, Eigenvectors, Eigenspaces, Diagonalisation, Cauley-Hamilton thoerem, Euclidean spaces, Orthogonality, Gram-Schmidt orthogonalization, Orthogonal matrices, Self-adjoint endomorphisms, Symmetric matrices, Spectral theorem, Isometries, Quadratic forms, Principal Axes, Square root of a nonnegative real symmetric matrix. Norms of a matrix.

Teaching and Learning Methods - Evaluation

Delivery

Classroom (face-to-face)

Use of Information and Communications Technology -
Teaching Methods
Activity Semester Workload
Lectures 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 resolving application problems.

Attached Bibliography

  • Introduction to Linear Algebra (Greek), Bozapalidis Symeon, ISBN: 978-960-99293-5-6 (Editor): Charalambos Nik. Aivazis
  • An Intorduction to Linear Algebra, 2012, (Greek) Varsos Dimitris, Deriziwtis Dimitris, Emmanouil Giannis, Maliakas Mixalis, Melas Antonios, Talleli Olympia ISBN: 978-960-6706-36-3 (Editor): “Sofia” Editions
  • Introduction to LINEAR ALGEBRA, 2006, Theodora Theochari, Hara Haralambous, Charilaos Vavatsoulas, (Greek) ISBN: 960-631-094-9, (Editor): Hara Charalambous
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