A brief history of the Singular value decomposition of matrices with some applications
Prof. Verma has been at IIT Bombay since 1990. He was Head of Mathematics Department (2006-2009) Chief Vigilance Officer (2011-2012) and Dean of Faculty Affairs during 2014-2016 and Institute Chair Professor during 2018-2021.
Prof. Verma has played a key-role in establishment of the National Centre of Mathematics in 2011 which is a joint Centre of TIFR and IIT Bombay. He has been its secretary and a member of its Apex Committee since 2011. He served as its Head during 2020-2023.
He has held visiting positions at Institute of Mathematics (Hanoi), Vietnam Institute of Advanced Studies (Hanoi), IIT Kharagpur, IISER Trivandrum, University of Essen (Germany) and University of Genoa (Italy). He is a member of the Academic Councils of Chennai Mathematical Institute (Chennai) and the National Institute of Science Education and Research (Bhubaneswar), Indraprasth Institute of Information technology, Delhi and IISER Berhampur. He has been the Secretary of the Ramanujan Mathematical Society (RMS) and he is currently the vice-president of the Mathematics Consortium of India and RMS.
In recognition of his research contributions, Prof. Verma was elected a Fellow of the National Academy of Sciences (Allahabad) in 2008 and a Fellow of the Indian National Science Academy in 2012. He was also a Fellow of the International Centre for Theoretical Physics during 2001-2007. He is a recipient of the IIT Bombay Excellence in Teaching Award in Mathematics in 2016 and the IIT Bombay S. P. Sukhatme award for excellence in teaching .
Prof. Verma has co-authored a text book Combinatorial Topology and Algebra and co-edited three proceedings of conferences. He has been a member of the editorial board of the Indian Journal of Pure and Applied Mathematics, Journal of the Indian Mathematical Society, Lecture Notes Series of Ramanujan Mathematical Society and the Bulletin of the Mathematics Teacher’s Association of India.
The singular value decomposition (SVD) of a matrix is a fundamental result in linear algebra and its applications in data science.
It produces good bases for the four fundamental subspaces associated with a real matrix A: the row and column spaces, the nullspace, and the nullspace of its transpose of A. The SVD produces a method to find the best approximation of A by matrices of lower rank. This Theorem has applications to data compression.
