Abstract
This article is part exposition of a recent rather technical paper of the last two authors on matrix pavings related to the 1959 Kadison-Singer Extension Problem and part a report on further computational results providing new bounds on the paving parameters for classes of small matrices investigated there and subsequently.
A website maintained by the authors provides to all interested the matrices experimentally discovered that yield these bounds along with the proprietary MATLAB software with simple operational directions to load them, pave them, and perform paving searches.
The convergence to 1 or not of the infinite sequences of these paving parameters in most cases is equivalent to the Kadison-Singer Extension Problem, and in all cases convergence to 1 negates the problem.
The last two sections describe the search process and an interpretation of the data integrated with the results of the precursor to this paper.
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Dedicated to Professor Richard V. Kadison on the Occasion of his 85th Birthday
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Schmidt, D., Weiss, G. & Zarikian, V. Paving small matrices and the Kadison-Singer Extension Problem II—computational results. Sci. China Math. 54, 2463–2472 (2011). https://doi.org/10.1007/s11425-011-4321-7
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DOI: https://doi.org/10.1007/s11425-011-4321-7