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

Abstract

Fingerprinting is a well known technique, which is often used in designing Monte Carlo algorithms for verifying identities involving ma- trices, 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 nxn matrices. The result is a Monte Carlo algorithm running in time $Theta(n^2)$ with an exponentially decreasing error probability after each indepen- dent 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.