Correction: 17 March 2005

Theorem 5 and Corollary 6 are FALSE (essentially, a divide-by-zero error in the proof).

(A) Correction:
M >= N+n  nec & suff generic invertibility when processing images, n=2.  May hold for larger n.


(B) Orders of the inverse?
Does there exist a left inverse with a given order? For polynomial orders, a conjecture:
Let "CVC" denote the criterion M*(a1+1)*(a2+1) >= N*(d1+a1+1)*(d2+a2+1),
where for index i=1,2 di and ai are the max orders of the polynomial matrix
and the left inverse, respectively.
Then, we conjecture that for M >= N+3, CVC both nec and sufficient for
generic existence of left inverse satisfying the given orders.




Update: 26 Sep 2008

Law, et al. give a nice proof of generalization of (A):  M-N >= n.
https://netfiles.uiuc.edu/kalaw/homepage/publications.htm
Law also gives a simpler construction using reduced Grobner basis.