Mathematics BSc
Course description
2013.
Course description
2013.
Applied linear algebra
Hours lect+pc 
Credits lect+pc 
Assessment  Specialization  Course code lect/pc 
Semester  Status 

2 + 2  2 + 3  exam + term grade 
applied math.  mm1c1la4e mm1c2la4e 
4  recommended 
Course coordinator
Strong  Weak  Prerequisites  

Practice class  
Strong:
Algebra2L
(mm1c1al2)
 
Strong:
Discrete matematics1L
(mm1c1vm1)
 
Lecture  
Weak:
practice class

Prerequisites
Classical and linear algebra, discrete mathematics, geometry.
Literature
 M. Aigner, G. M. Ziegler: Proofs from the Book. Springer, 2009.
 P. D. Lax: Linear algebra and its applications. Wiley, 2007.
Syllabus
 Algebraic applications. Generalized inverses, application of generalized inverses to solutions of systems of linear equations (exact solution and best approximation). Jordan normal form, taking the power of matrices, solving linear recurrences, Markov chains. Positive matrices, stochastic matrices, the PerronFrobenius theorem. Fast matrix multiplication.
 Applications in graph theory. Graphs and associated matrices. The CauchyBinet formula. The number of spanning trees, Cayley's theorem about the number of labelled trees. Catalan numbers. Shannon capacity.
 Geometric and combinatorial applications. Volume and determinants. Applications of Vandermonde's determinant. The solution of Hilbert's third problem: Dehn's theorem about equidecomposability. Points sets with a small number of distances. Extremal set theory, block systems.