Bounds on sample space size for matrix product verification

We show that the size of any sample space that could be used in Freivalds' probabilistic matrix product verification algorithm for n × n matrices is at least ( n − 1)/ ε if the probability of error is at most ε, matching the upper bound of Kimbrel and Sinha. We also provide a characterization of any sample space for which Freivalds' algorithm has probability of error at most ε. We then provide a generalization of Freivalds' algorithm and give a tight lower bound on the time-randomness tradeoff for this class of algorithms.