A Simplified Proof For The Application Of Freivalds' Technique to Verify Matrix Multiplication

Fingerprinting is a well known technique, which is often used in designing Monte Carlo algorithms for verifying identities involving matrices, integers and polynomials. The book by Motwani and Raghavan [1] shows how this technique can be applied to check the correctness of matrix multiplication – check if AB = C where A,B and C are three n×n matrices. The result is a Monte Carlo algorithm running in time Θ(n) with an exponentially decreasing error probability after each independent iteration. In this paper we give a simple alternate proof addressing the same problem. We also give further generalizations and relax various assumptions made in the proof.