In statistics, two-sample tests are commonly desired under many topics. It's crucial to differentiate populations as a prerequisite for developing further analysis. A number of statistical tests have been developed for this hypothesis testing problem. In this thesis, we propose a novel method to perform two-sample test. Specifically, we use the two samples to form a matrix and adopt the largest eigen-value as the test statistic. This test statistic followed the tracy-widom law as the limiting distribution under the null hypothesis. We evaluate the performance of the proposed method by extensive simulation study and real data application. The type I error is consistently and asymptotically controlled to nominal level. Our test manifests competitive power and prevailing calculation cost compared with several well-known two-sample test methods. The real data application also shows the advantage of the proposed method.