It is well known that the set of all square invertible real matrices has two connected components. The set of all m×n rectangular real matrices of rank r has only one connected component when m ≠ 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.
|Original language||English (US)|
|Number of pages||7|
|Journal||Proceedings of the American Mathematical Society|
|State||Published - Feb 1994|