Linear Algebra (N3)

Module Notes
Faculty Member (Members):
Undergraduate, 2nd Semester (1st Year, Spring)
Module Category: Compulsory Modules
Module Type: Background Courses
Teaching Language: Greek
Course Code: CHM_100n
Credits: 3
ECTS Credits: 7
Teaching Type: Lectures (2h/W) Τutorial (1h/W)
Module Availability on Erasmus Students: No
Course URL: ChemEngUP / e-class
Student's office hours: Friday 09.00 - 13.00
Module Details

At the end of this course the student should be able to:

  1. Have a good understanding of the knowledge of the basic applied mathematics for engineers, within the wide area of the linear algebra, which is adequate to his/her science.
  2. Know the new notions in the form of definitions and theorems that concern the basic contents of the course "Linear Algebra", in order to be able to apply them.
  3. Combine and make worthy of the knowledge that he/she acquired to other fields of the theoretical and applied mathematics, in which certain notions and principles of the present course are necessary and useful.

At the end of the course the student will have further developed the following skills and competences:

  1. Ability to demonstrate knowledge and understanding of essential concepts, principles and applications that are related to the linear algebra.
  2. Ability to apply such knowledge to the solution of problems in other fields of the wide conception of theoretical and applied mathematics, related to the science of Chemical Engineering, or to the solution of multidisciplinary problems.
  3. Study skills needed for continuing profession development.

There are no prerequisite courses. It is, however, recommended that students should have the basic knowledge, which they were taught to the corresponding part of the course "Single Variable Calculus".

Set of real and complex matrices, general matrix theory and square matrices, types of matrices. Determinant and properties, inverse matrix. Vector spaces and subspaces, intersection and simple sum of subspaces. Linear dependence and independence, generators. Basis and extension of basis, dimension and direct sum of subspaces. Coordinate vector and change of basis in a vector space. Homogeneous and non-homogeneous systems of linear equations, investigation of square systems and vector space of solutions, general solution with Gauss elimination method. Alternative methods for square systems, Crammer method and method of inverse matrix. Spectral analysis of a square matrix, eigenvalues and eigenvectors or characteristic elements and geometrical meaning, Cayley-Hamilton theorem. Algebraic and geometric multiplicity of eigenvalues and degree of degeneration, diagonalization of a square matrix. Degenerate eigenvalues and generalized eigenvectors, square Jordan matrix. Vector spaces of inner product and norm, sets of metric spaces and distance, conceptions and physical meaning. Orthogonality, normality and orthonormalization with Gram-Schmidt method.

Use of web pages and e-class.

  1. Teaching (2 hours/week): lectures using blackboard of the theory and its application to typical mathematical problems of Chemical Engineering.
  2. Recitation (1 hour/week): solving on the blackboard exercises concerning mainly mathematical applications of the science of Chemical Engineering.

Total Module Workload (ECTS Standards):

204 Hours

The instruction language is Greek and the evaluation includes optional exercise series and written or / and oral examination (100% of final mark).

  1. D.C. Lay, S.R. Lay and J.J. McDonald, "Linear Algebra and Applications" (general editing & translation P. Vafeas, N. Labropoulos), Broken Hill Publishers Ltd, Nicosia, 2022 (Eudoxos / code 112690641).
  2. G. Strang, "Linear Algebra and Applications" (translation A. Chortaras - scientific editing P. Pamfilos), University of Crete Press, Heraklion, 2025 (Eudoxos / code 102074431).