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  • 2010.14429v2

    Accepted author manuscript, 323 KB, PDF document

    Available under license: Other

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Matrix compression along isogenic blocks

Research output: Contribution to Journal/MagazineJournal articlepeer-review

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<mark>Journal publication date</mark>18/03/2022
<mark>Journal</mark>Acta Scientiarum Mathematicarum
Number of pages30
Publication StatusAccepted/In press
<mark>Original language</mark>English

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.