The set of all rectangular real matrices of rank 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 rectangular real matrices of rank has only one connected component when or . We show that all these connected components are connected by analytic regular arcs. We apply this result to establish the existence of -times differentiable bases of the kernel and the image of a rectangular real matrix function of several real variables.

**[1]**Klaus Deimling,*Nonlinear functional analysis*, Springer-Verlag, Berlin, 1985. MR**787404****[2]**Jean-Claude Evard,*On the existence of bases of class 𝐶^{𝑝} of the kernel and the image of a matrix function*, Linear Algebra Appl.**135**(1990), 33–67. MR**1061529**, 10.1016/0024-3795(90)90115-S**[3]**J.-Cl. Evard and F. Jafari,*Polynomial path connectedness and Hermite interpolation in topological vector spaces*, submitted.

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DOI:
http://dx.doi.org/10.1090/S0002-9939-1994-1189542-9

Article copyright:
© Copyright 1994
American Mathematical Society