The set of all πΓπ rectangular real matrices of rank π is connected by analytic regular arcs
J.-Cl. Evard, Farhad Mohammad Jafari Β· Proceedings of the American Mathematical Society Β· 1994
It is well known that the set of all square invertible real matrices has two connected components. The set of all m Γ n m \times n rectangular real matrices of rank r r has only one connected component when m β n m e n or r > m = n 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 p -times differentiable bases of the kernel and the image of a rectangular real matrix function of several real variables.