Reverse Cholesky factorization and tensor products of nest algebras
Functional Analysis
2017-04-17 v1
Abstract
We prove that every positive semidefinite matrix over the natural numbers that is eventually 0 in each row and column can be factored as the product of an upper triangular matrix times a lower triangular matrix. We also extend some known results about factorization with respect to tensor products of nest algebras. Our proofs use the theory of reproducing kernel Hilbert spaces.
Cite
@article{arxiv.1704.04323,
title = {Reverse Cholesky factorization and tensor products of nest algebras},
author = {Vern I. Paulsen and Hugo J. Woerdeman},
journal= {arXiv preprint arXiv:1704.04323},
year = {2017}
}