Changes
Combinatorica 25, pp 187-215 (2005) [http://dx.doi.org/10.1007/s00493-005-0013-7 DOI link] [http://www.math.uwaterloo.ca/~jfgeelen/publications/iwata.ps PDF]</ref> studied the rank of "T+K" where "T" is the Tutte matrix of a graph, and "K" is a [[wikipedia:skew symmetric matrix|skew symmetric ]] constant matrix. This modest generalization already turns out to be equivalent to the so called linear delta-matroid parity problem.
One might be interested not only in deciding whether a polynomial matix matrix is nonsingular, but also in (deterministically) finding
an evaluation with nonzero determinant, if there exists such. (The Schwartz-Zippel lemma
shows that there are indeed only a very few evaluations with zero determinant for a nonsingular matrix). For the Tutte-matrix, Geelen<ref>J. Geelen, An algebraic matching algorithm,
Combinatorica 20, pp 61-70 (2000) [http://dx.doi.org/10.1007/s004930070031 DOI link] [http://www.math.uwaterloo.ca/~jfgeelen/publications/match.ps PS]</ref> gave a deterministic polynomial-time algorithm.
