A generalization of Rohn's theorem on full-rank interval matrices

ABSTRACT

A general closed interval matrix is a matrix whose entries are closed connected nonempty subsets of $\mathbb{R}$, while an interval matrix is defined to be a matrix whose entries are closed bounded nonempty intervals in $\mathbb{R}$. We say that a matrix A with constant entries is contained in a general closed interval matrix μ if, for every i,j, we have that $A_{i,j}\in {\mu }_{i,j}$. Rohn characterized full-rank square interval matrices, that is, square interval matrices μ such that every constant matrix contained in μ is nonsingular. In this paper, we generalize this result to general closed interval matrices.

COMMUNICATED BY:

• R. Loewy

KEYWORDS:

• Interval matrices
• rank

2010 MATHEMATICAL SUBJECT CLASSIFICATION::

• 15A99
• 15A03

Acknowledgements

This work was supported by the National Group for Algebraic and Geometric Structures and their Applications (GNSAGA-INdAM).

Disclosure statement

No potential conflict of interest was reported by the author.