COMMUNICATION COMPLEXITY OF MATRIX COMPUTATION OVER FINITE-FIELDS

We investigate the communication complexity of singularity testing in a finite field, where the problem is to determine whether a given square matrix M is singular. We show that, for n x n matrices whose entries are elements of a finite field of size p, the communication complexity of this problem is Theta(n(2) log p). Our results imply tight bounds for several other problems like determining the rank and computing the determinant.