The set of all $m\times n$ rectangular real matrices of rank $r$ is connected by analytic regular arcs
HTML articles powered by AMS MathViewer
- by J.-Cl. Evard and F. Jafari PDF
- Proc. Amer. Math. Soc. 120 (1994), 413-419 Request permission
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.References
- Klaus Deimling, Nonlinear functional analysis, Springer-Verlag, Berlin, 1985. MR 787404, DOI 10.1007/978-3-662-00547-7
- 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, DOI 10.1016/0024-3795(90)90115-S J.-Cl. Evard and F. Jafari, Polynomial path connectedness and Hermite interpolation in topological vector spaces, submitted.
Additional Information
- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 120 (1994), 413-419
- MSC: Primary 15A54; Secondary 54D05
- DOI: https://doi.org/10.1090/S0002-9939-1994-1189542-9
- MathSciNet review: 1189542