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

Comments

First published in Proceedings of the American Mathematical Society 120.2 (Feb 1994), published by the American Mathematical Society. Available at http://www.jstor.org/stable/2159876.

Included in

Mathematics Commons

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