We will introduce basic non-asymptotic methods and
concepts in random matrix
theory. The students will learn tools for the analysis of the extreme
singular values
of random matrices with independent rows or columns. They results have
applications in several fields, most notably in theoretical computer
science, statistics and
signal processing.
Last update: T_KMA (16.04.2015)
Představíme základní neasymptotické metody a koncepty
teorie náhdoných matic.
Studenti poznají nástroje pro analýzu extrémních singulárních čísel
náhodných matic
s nezávislými řádky či sloupci. Tyto výsledky mají aplikace v řadě oborů,
zejména v teoretické informatice, statistice a zpracování signálů.
Literature -
Last update: doc. RNDr. Dr. rer. nat. Jan Vybíral, Ph.D. (28.07.2015)
Roman Vershynin, Introduction to the non-asymptotic analysis of random matrices, 2011
Joel Tropp, User-friendly tail bounds for sums of random matrices, 2012
Joel Tropp, An Introduction to Matrix Concentration Inequalities, 2015
Terry Tao, Topics in random matrix theory, 2012
Last update: doc. RNDr. Dr. rer. nat. Jan Vybíral, Ph.D. (28.07.2015)
Roman Vershynin, Introduction to the non-asymptotic analysis of random matrices, 2011
Joel Tropp, User-friendly tail bounds for sums of random matrices, 2012
Joel Tropp, An Introduction to Matrix Concentration Inequalities, 2015
Terry Tao, Topics in random matrix theory, 2012
Syllabus -
Last update: T_KMA (16.04.2015)
1. Introduction: matrices, singular values, sub-gaussian random variables, sub-exponential random variables, isotropic random vectors
2. Sums of independent random matrices
3. Random matrices with independent entries
4. Random matrices with independent rows and columns