One of discussions in multivariable analysis is defining the factor and main vectors by calculating eigenvalue. In this paper we deal with an unbiased estimator of eigenvector and as a result we define eigenvalues. The purpose was introducing a new statistical method that is different from other numerical methods, which it defines the eigenvalue matrix. On the other hand, the efficiency of this method is up when the mass and dimension of matrix are high. Therefore, this is a low cast and efficient method in calculation. This paper covers some background of data compression and how Markov chain Monte Carlo (MCMC) and principal component analysis (PCA) has been and can be used for calculating eigenvalue.