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In 2019 Skoltech, Marchuk Institute of Numerical Mathematics, RAS and Huawei Technologies Co. Ltd. are organizing 5-th International Conference on Matrix Methods in Mathematics and applications (MMMA-2019). Nowadays, matrix methods are in very core of modern numerical mathematics, computational fluid dynamics, machine learning and many other spheres of science and applications. Novel results in this field of research may have influence on life of extremely broad community of researchers, engineers and commercial companies. The aim of this conference is to present and discuss recent results in development of matrix methods, numerical linear algebra, tensor decompositions in both fundamental and applied scopes. We have invited top active researchers working in corresponding fields of science of Russia and also from Switzerland, Germany, Italy, UK, USA and other countries. Each speaker will present original work as well as significant work-in-progress covering novel theories, methods and meaningful applications. This workshop is an opportunity to bring together academic and industrial scientists to discuss the recent advances. The topics of interest include but not limited to: Matrix factorizations Tensor decompositions Modelling of problems in higher dimensions Tensor networks Application of matrix methods in machine learning Parallel algorithms Invited speakers: Victor Pan, Lehman College, CUNY Nicola Mastronardi, Instituto per le Applicazioni del Calcolo Walter Gander, ETH Zurich Andrzej Cichocki, Skoltech Vladimir Kazeev, Stanford University Vladimir Druskin, Worcester Polytechnic Institute Dario Fasino, University of Udine Sergey Dolgov, University of Bath Carmine Di Fiore, University of Rome "Tor Vergata" Lidia Aceto, University of Pisa Boris Khoromskij, Max Plank Institute Venera Khoromskaia, Max Plank Institute Michela Redivo-Zaglia, University of Padova Reinold Schneider, TU Berlin Volker Mehrmann, TU Berlin Valery P. Ilin, Novosibirsk, RAS Raymond Chan, City university of Hong Kong