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 ${I}_{n}$ can be continuously factorized through a continuous $N×N$ matrix function $A$ with domain in $ℝ$. 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 ${I}_{n}$ through $A$.

Keywords
factorization of the identity, matrices with large diagonal
Mathematical Subject Classification 2010
Primary: 15A23, 46B07