Belton, A and Guillot, D and Khare, A and Putinar, M (2022) Matrix compression along isogenic blocks. In: Acta Scientiarum Mathematicarum, 88 (1-2). pp. 417-448.
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Abstract
A matrix-compression algorithm is derived from a novel isogenicblock decomposition for square matrices. The resulting compression andinflation operations possess strong functorial and spectral-permanenceproperties. The basic observation that Hadamard entrywise functionalcalculus preserves isogenic blocks has already proved to be of paramountimportance for thresholding large correlation matrices. The proposedisogenic stratification of the set of complex matrices bears similarities tothe Schubert cell stratification of a homogeneous algebraic manifold. Anarray of potential applications to current investigations in computationalmatrix analysis is briefly mentioned, touching concepts such as symmetricstatistical models, hierarchical matrices and coherent matrix organizationinduced by partition trees. © 2022, The Author(s).
| Item Type: | Journal Article |
|---|---|
| Publication: | Acta Scientiarum Mathematicarum |
| Publisher: | Springer Nature |
| Additional Information: | The copyright for this article belongs to the Authors. |
| Keywords: | 14M15; 15A86; 47A60; 65F45; 65F55; conditional expectation; Hadamard calculus; matrix compression; structured matrix |
| Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |
| Date Deposited: | 21 Feb 2023 04:47 |
| Last Modified: | 21 Feb 2023 04:47 |
| URI: | https://eprints.iisc.ac.in/id/eprint/80573 |
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