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Mathematics > Numerical Analysis

arXiv:2305.00485 (math)
[Submitted on 30 Apr 2023 (v1), last revised 27 Sep 2023 (this version, v2)]

Title:Representing the Special Linear Group with Block Unitriangular Matrices

Authors:John Urschel
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Abstract:We prove that every element of the special linear group can be represented as the product of at most six block unitriangular matrices, and that there exist matrices for which six products are necessary, independent of indexing. We present an analogous result for the general linear group. These results serve as general statements regarding the representational power of alternating linear updates. The factorizations and lower bounds of this work immediately imply tight estimates on the expressive power of linear affine coupling blocks in machine learning.
Subjects: Numerical Analysis (math.NA)
MSC classes: 15A23
Cite as: arXiv:2305.00485 [math.NA]
  (or arXiv:2305.00485v2 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2305.00485

Submission history

From: John C Urschel [view email]
[v1] Sun, 30 Apr 2023 14:02:00 UTC (8 KB)
[v2] Wed, 27 Sep 2023 01:20:07 UTC (13 KB)
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