Abstract
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) |
|---|---|
| Pages (from-to) | 413-419 |
| Number of pages | 7 |
| Journal | Proceedings of the American Mathematical Society |
| Volume | 120 |
| Issue number | 2 |
| DOIs | |
| State | Published - Feb 1994 |
| Externally published | Yes |