Vol. 13, No. 1, 2020

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Continuous factorization of the identity matrix

Yuying Dai, Ankush Hore, Siqi Jiao, Tianxu Lan and Pavlos Motakis

Vol. 13 (2020), No. 1, 149–164
Abstract

We investigate conditions under which the identity matrix In can be continuously factorized through a continuous N × N matrix function A with domain in . We study the relationship of the dimension N, the diagonal entries of A, and the norm of A to the dimension n and the norms of the matrices that witness the factorization of In through A.

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Keywords
factorization of the identity, matrices with large diagonal
Mathematical Subject Classification 2010
Primary: 15A23, 46B07
Milestones
Received: 31 August 2019
Revised: 7 October 2019
Accepted: 14 October 2019
Published: 4 February 2020

Communicated by Kenneth S. Berenhaut
Authors
Yuying Dai
Department of Mathematics
University of Illinois at Urbana-Champaign
Urbana, IL
United States
Ankush Hore
Department of Mathematics
University of Illinois at Urbana-Champaign
Urbana, IL
United States
Siqi Jiao
Department of Mathematics
University of Illinois at Urbana-Champaign
Urbana, IL
United States
Tianxu Lan
Department of Mathematics
University of Illinois at Urbana-Champaign
Urbana, IL
United States
Pavlos Motakis
Department of Mathematics
University of Illinois at Urbana-Champaign
Urbana, IL
United States