Accepted author manuscript, 323 KB, PDF document
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Accepted author manuscript
Licence: Other
Final published version
Licence: CC BY: Creative Commons Attribution 4.0 International License
Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Matrix compression along isogenic blocks
AU - Belton, Alexander
AU - Guillot, Dominique
AU - Khare, Apoorva
AU - Putinar, Mihai
PY - 2022/8/31
Y1 - 2022/8/31
N2 - 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.
AB - 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.
U2 - 10.1007/s44146-022-00023-0
DO - 10.1007/s44146-022-00023-0
M3 - Journal article
VL - 88
SP - 417
EP - 448
JO - Acta Scientiarum Mathematicarum
JF - Acta Scientiarum Mathematicarum
SN - 0001-6969
IS - 1-2
ER -