Matrix compression along isogenic blocks

Belton, Alexander and Guillot, Dominique and Khare, Apoorva and Putinar, Mihai (2022) Matrix compression along isogenic blocks. Acta Scientiarum Mathematicarum. ISSN 0001-6969 (In Press)

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Abstract

A matrix-compression algorithm is derived from a novel isogenic block decomposition for square matrices. The resulting compression and inflation operations possess strong functorial and spectral-permanence properties. The basic observation that Hadamard entrywise functional calculus preserves isogenic blocks has already proved to be of paramount importance for thresholding large correlation matrices. The proposed isogenic stratification of the set of complex matrices bears similarities to the Schubert cell stratification of a homogeneous algebraic manifold. An array of potential applications to current investigations in computational matrix analysis is briefly mentioned, touching concepts such as symmetric statistical models, hierarchical matrices and coherent matrix organization induced by partition trees.

Item Type:
Journal Article
Journal or Publication Title:
Acta Scientiarum Mathematicarum
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2600/2604
Subjects:
ID Code:
168825
Deposited By:
Deposited On:
14 Apr 2022 13:55
Refereed?:
Yes
Published?:
In Press
Last Modified:
21 May 2022 00:55