Reverse Cholesky factorization and tensor products of nest algebras

Paulsen, Vern; Woerdeman, Hugo

doi:10.1090/proc/13851

Reverse Cholesky factorization and tensor products of nest algebras
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by Vern I. Paulsen and Hugo J. Woerdeman PDF

Proc. Amer. Math. Soc. 146 (2018), 1693-1698 Request permission

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.

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