FoCM 2014 conference

Workshop C4 - Numerical Linear Algebra - Semi-plenary talk

December 18, 17:05 ~ 17:55 - Room B11

## Factoring arbitrary matrices into products of structured matrices

### Lek-Heng Lim

### University of Chicago, USA - lekheng@galton.uchicago.edu

We show that every $n\times n$ matrix can be decomposed into (i) a product of $n/2 $ Toeplitz matrices, (ii) a product of $n/2$ Hankel matrices, (iii) a product of $4n$ Vandermonde matrices, (iv) a product of $16n$ bidiagonal matrices, or (v) a product of $n^2$ companion matrices. We will see that such decompositions do not in general hold with other types of structured matrix factors (e.g. circulant, symmetric Toeplitz, persymmetric Hankel, etc).

Joint work with Ke Ye (University of Chicago, USA).