#### Document Type

Article

#### Publication Date

2-1-1994

#### Abstract

It is well known that the set of all square invertible real matrices has two connected components. The set of all m x n rectangular real matrices of rank r has only one connected component when m not-equal n or r < m = n . We show that all these connected components are connected by analytic regular arcs. We apply this result to establish the existence of p-times differentiable bases of the kernel and the image of a rectangular real matrix function of several real variables.

#### Publication Title

Proceedings of the American Mathematical Society

#### DOI

10.2307/2159876

#### Publication Information

Evard, J. C. and Jafari, Farhad (1994). "The Set of All MXN Rectangular Real Matrices of Rank-R Is Connected by Analytic Regular Arcs." *Proceedings of the American Mathematical Society *120.2, 413-419.

## Comments

First published in

Proceedings of the American Mathematical Society120.2 (Feb 1994), published by the American Mathematical Society. Available at http://www.jstor.org/stable/2159876.