Klyachko, A.A.2016-02-082016-02-082000243795http://hdl.handle.net/11693/24979Using harmonic analysis on symmetric spaces we reduce the singular spectral problem for products of matrices to the recently solved spectral problem for sums of Hermitian matrices. This proves R.C. Thompson's conjecture [Matrix Spectral Inequalities, Johns Hopkins University Press, Baltimore, MD, 1988]. © 2000 Elsevier Science Inc.EnglishEigenvaluesRandom walksSingular valuesSpherical functionsArticle