Computational complexity of some problems of linear algebra

Abstract

The computational complexity of some problems dealing with matrix rank is addressed. Depending on the subsets of a given commutative ring, the complexity of these problems can range from polynomial-time solvable to random polynomial-time solvable to NP-complete to PSPACE-solvable to unsolvable. An approximation version of the minrank problem is shown to be MAXSNP-hard.