Linear Algebra II (MAY221)

Undergraduate Courses Outlines - Department of Mathematics

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