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A panorama of positivity. Ii: Fixed dimension

Belton, A and Guillot, D and Khare, A and Putinar, M (2020) A panorama of positivity. Ii: Fixed dimension. [Book Chapter]

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Official URL: https://doi.org/10.1090/conm/743/14958


This survey contains a selection of topics unified by the concept of positive semidefiniteness (of matrices or kernels), reflecting natural constraints imposed on discrete data (graphs or networks) or continuous objects (probability or mass distributions). We put emphasis on entrywise operations which preserve positivity, in a variety of guises. Techniques from harmonic analysis, function theory, operator theory, statistics, combinatorics, and group representations are invoked. Some partially forgotten classical roots in metric geometry and distance transforms are presented with comments and full bibliographical references. Modern applications to high-dimensional covariance estimation and regularization are included. © 2020 American Mathematical Society.

Item Type: Book Chapter
Publication: Contemporary Mathematics
Publisher: American Mathematical Society
Additional Information: The copyright for this article belongs to American Mathematical Society
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 19 Apr 2021 07:34
Last Modified: 19 Apr 2021 07:34
URI: http://eprints.iisc.ac.in/id/eprint/68662

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