Temple Univeristy Mathematics Colloquium

Monday, April 24, 2017 - 4:00pm to 6:00pm

Gilbert Strang

MIT

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. For several one-zero matrices we have open questions about the rank. Alex Townsend has identified an important class of large matrices that have rapidly decaying singular values --- allowing superfast algorithms.