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 (Gram-Schmidt, 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
- Gramm-Schmidt procedure, QR factorization, The singular value decomposition
- General inner-product 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: Linear Algebra and its Applications (Fifth edition), David C. Lay, Steven R. Lay, Judi McDonald – ISBN-10: 1-292-09223-8.
- Handouts (via Blackboard).