Applied linear algebra
|2 + 2||2 + 3||exam +
Discrete matematics1L (mm1c1vm1)
Syllabus designed by:
Classical and linear algebra, discrete mathematics, geometry.
- M. Aigner, G. M. Ziegler: Proofs from the Book. Springer, 2009.
- P. D. Lax: Linear algebra and its applications. Wiley, 2007.
- 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 Perron-Frobenius theorem. Fast matrix multiplication.
- Applications in graph theory. Graphs and associated matrices. The Cauchy-Binet 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.