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Reverse Cholesky factorization and tensor products of nest algebras


Authors: Vern I. Paulsen and Hugo J. Woerdeman
Journal: Proc. Amer. Math. Soc. 146 (2018), 1693-1698
MSC (2010): Primary 47A46, 47A68
DOI: https://doi.org/10.1090/proc/13851
Published electronically: December 4, 2017
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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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Additional Information

Vern I. Paulsen
Affiliation: Institute for Quantum Computing and Department of Pure Mathematics, University of Waterloo, 200 University Avenue West, Waterloo, Ontario, Canada N2L 3G1
Email: vpaulsen@uwaterloo.ca

Hugo J. Woerdeman
Affiliation: Department of Mathematics, Drexel University, 3141 Chestnut Street, Philadelphia, Pennsylvania, 19104
Email: hugo@math.drexel.edu

DOI: https://doi.org/10.1090/proc/13851
Received by editor(s): April 13, 2017
Received by editor(s) in revised form: June 16, 2017
Published electronically: December 4, 2017
Additional Notes: The first author was partially supported by an NSERC grant. The second author was partially supported by Simons Foundation grant 355645, and the Institute for Quantum Computing at the University of Waterloo.
Communicated by: Stephan Ramon Garcia
Article copyright: © Copyright 2017 American Mathematical Society

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