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Course module: 35B801-B-6
35B801-B-6
Advanced Linear Algebra
Course info
Course module35B801-B-6
Credits (ECTS)6
CategoryBA (Bachelor)
Course typeCourse
Language of instructionEnglish
Offered byTilburg University; Tilburg School of Economics and Management; TiSEM: Econometrics and OR; Econometrics & Operations;
Is part of
B Econometrics and Operations Research
B Economics and Business Economics
Contact persondr. C. Dobre
Lecturer(s)
Coordinator course
dr. C. Dobre
Other course modules lecturer
Lecturer
dr. C. Dobre
Other course modules lecturer
Lecturer
dr.ir.ing. M.J.P. Peeters
Other course modules lecturer
Lecturer
P. Wissing, MSc
Other course modules lecturer
Academic year2019
Starting block
SM 1
Course mode
Full-time
Remarks-
Registration openfrom 19/08/2019 up to and including 24/01/2020
Aims

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.
Content

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
  1. Compulsory reading: Linear Algebra and its Applications (Fifth edition), David C. Lay, Steven R. Lay, Judi McDonald – ISBN-10: 1-292-09223-8. 

  2. Handouts (via Blackboard).
Course available for exchange students
Conditions of admission apply
Timetable information
Advanced Linear Algebra
Required materials
-
Recommended materials
-
Tests
Written exam

Final grade

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Kies de Nederlandse taal