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).