
The aim of this course is to extend the knowledge obtained during the first year course “Linear Algebra”, thus enabling students to comfortably work with the tougher properties of matrices and matrix spaces in order to easily broaden their optimization techniques in future EOR courses like: “Combinatorial Optimization” and “Operations Research Methods”. As “Linear Algebra” course was vital for the “Linear Optimization” course, so will “Advanced Linear Algebra” be for the above mentioned courses and various other topics in the EOR bachelor program or the “Business Analytics and Operations Research” master program.
After completing this course students should be able to:
 use the eigenvalue, eigenvector and eigenspace properties for optimization and dynamical systems
 use numerical procedures (GramSchmidt, QR factorization, diagonalization techniques) to compute eigenvalues, eigenvectors and eigenspaces
 think critically about working with matrix spaces, namely cones of matrices;
 recognize the burden that numerical computations bring when working with matrices instead of real numbers.



Topics to be covered include:
 Eigenvalues and the characteristic polynomial
 Basis and coordinates. The matrix of a linear transformation.
 Complex eigenvalues. The Main Theorem of Algebra. Jordan form of a matrix.
 Linear difference equations and vector recurrence equations
 GrammSchmidt procedure, QR factorization, The singular value decomposition
 General innerproduct spaces
 Quadratic forms and positive semidefinite matrices
 Principal component analysis
 Cones and dual cones
Type of instructions
2 hours lecture per week and 2 hours tutorials per week
Type of exams
written exam (weight 100%)
Compulsory Reading

Compulsory reading: Linear Algebra and its Applications (Fifth edition), David C. Lay, Steven R. Lay, Judi McDonald – ISBN10: 1292092238.
 Handouts (via Blackboard).




Course available for exchange students 
Conditions of admission apply 
  Required materialsRecommended materialsTestsWritten exam
 Final grade


 