In this “something for everyone” talk, we will place the matrix decompositions that are so valuable in all fields of computation in a historical abstract context.  It is well known that the singular value decomposition was discussed as far back as the 19th century by Beltrami and Jordan. Lesser known is that Cartan had a blueprint for matrix decompositions in 1927, that seems to be extended by Harish–Chandra in 1956 and further by Flensted–Jensen in 1978.

We will discuss the interesting history, speculating on why much of this work remains not very well known in applied settings,  and build on this work to obtain 53 matrix factorizations (and more) many of which appear to be new. We also provide a completed Random Matrix Theory connecting famous random matrix distributions to the geometry of symmetric spaces.

This is joint work with Sungwoo Jeong.

Professor Edelman considers himself to be a pure mathematician and an applied computer scientist. He works in the areas of numerical linear algebra, Random Matrix theory, high performance computing systems, networks, software, and algorithms.  He has won many prizes for his work including the prestigious Gordon Bell Prize, the Householder prize, the Sidney Fernbach award, and Babbage Prize. He was the founder of Interactive Supercomputing, a company acquired by Microsoft in its fifth year employing nearly 50 people, and is a co-creator of Julia. He is an elected fellow of ACM, AMS, IEEE, and SIAM. He believes above all that math and computing go together and both should be fun.

Organizer: dvzenkov@ncsu.edu