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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The set of all $ m\times n$ rectangular real matrices of rank $ r$ is connected by analytic regular arcs


Authors: J.-Cl. Evard and F. Jafari
Journal: Proc. Amer. Math. Soc. 120 (1994), 413-419
MSC: Primary 15A54; Secondary 54D05
MathSciNet review: 1189542
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Abstract: It is well known that the set of all square invertible real matrices has two connected components. The set of all $ m \times n$ rectangular real matrices of rank $ r$ has only one connected component when $ m \ne 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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1994-1189542-9
PII: S 0002-9939(1994)1189542-9
Article copyright: © Copyright 1994 American Mathematical Society