#### 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 $A$.

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