@ Florida State University

March 18-19, 2017

MIT

Gilbert Strang was an undergraduate at MIT and a Rhodes Scholar at Balliol College, Oxford. His Ph.D. was from UCLA and since then he has taught at MIT. He is a member of the National Academy of Sciences and he has published eleven books:

- Differential Equations and Linear Algebra (2014)
- Introduction to Linear Algebra (1993,1998,2003,2009)
- Linear Algebra and Its Applications (1976,1980,1988,2005)
- An Analysis of the Finite Element Method, with George Fix (1973, 2008)
- Introduction to Applied Mathematics (1986)
- Calculus (1991)
- Wavelets and Filter Banks, with Truong Nguyen (1996)
- Linear Algebra, Geodesy, and GPS, with Kai Borre (1997)
- Computational Science and Engineering (2007)
- Essays in Linear Algebra (2012)
- Algorithms for Global Positioning, with Kai Borre (2012)

Title: Singular Values of Large Matrices

The "fundamental theorem of linear algebra" tells us about orthogonal bases for the row space and column space of any matrix. More than that, it identifies the most important part of the matrix --- which is a central goal for a matrix of data. Since data matrices are normally rectangular, singular values must replace eigenvalues.

This talk will be partly about the underlying theory and partly about some of its applications to understanding what the matrix tells us. Alex Townsend has identified an important class of large matrices that have rapidly decaying singular values --- allowing superfast algorithms.