Hello, let C be the set of all m x n real matrices with rank equal to m. Consider C with the usual euclidean metric of R^(m*n). Does there exist a continuous map f:C x R^m -> R^n such that A*f(A,y) = y for every A in C and y in R^m?
The answer seems to be obviouslt yes, but I couldn't find a proof. Do you have some idea?
Thank you very very much for your attention. My Best Regards, Maury Barbato