Linear Algebra

Course Code: N2-1030
Weekly Duty: 4 (2Th + 2E)
ECTS: 6
Typical Semester: 1rst
Course Category: General Infrastructure Course
Prerequisites:  

Course Content
  1. Introduction : Vectors, Matrices (transpose, inverse, etc), the Determinant of a matrix
  2. Vector Space (VS), Linear independence (dependence), Subspace of a VS, orthogonal complement of a VS.
  3. Linear Span
  4. Base of VS, “replacement” Theorem, orthonormal base
  5. Eucledean VS, Schwarz inequality, Pythagorean Theorem in Rn
  6. Orthonormaliztion of a set of vectors (Gram, Schmidt), Orthogonal projection
  7. Change of the Base
  8. Linear Transformations, Linear Simultaneous Equations ( Isomorphism)
  9. Invariant Subspaces (Eigenvalues, Eigenvectors), Related theory
  10. Homogeneous Coordinates, Examples
  11. General Quadratic Forms (GQF) and Applications to Geometry (Invariant Quantities etc), Evaluating GQF through homogeneous coordinates
  12. Tangent Line and Tangent Plane to GQF
  13. Study the Cycle, Sphere, Ellipse, Ellipsoidal
  14. The Least Square Method (LSM) and Orthogonal Projection – general form of the normal equations
  15. Exercises and applications to all above mentioned

Literature
  1. Γλαμπεδάκης, Μ. Γλαμπεδάκης Α. (2014). Γραμμική Άλγεβρα. Εκδ Ιων.
  2. Χ. Π. Κίτσος (2011) Τεχνολογικά Μαθηματικά και Στατιστική Ι. Εκδ. Νέων Τεχνολογιών.
  3. Amir-Moez, A. R, and Fass, A. L. (1962). Elements of Linear Spaces. Pergamon Press.
  4. Παπαγεωργίου, Γ., Τσίτουρας, Χ., Φαμέλης, Ι. (2004). Σύγχρονο Μαθηματικό Λογισμικό MATLAB-MATHEMATICA. Εκδόσεις Συμεών.
  5. Steven J.L. (2006), Linear Algebra With Applications (7th ed.), Pearson Prentice Hall.
  6. Sheldon, A. (2004), Linear Algebra Done Right (2nd ed.). Springer.

Internationalisation I18n