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Estimating of Eigenvalue with Monte Carlo Method and its Application in the Principal Components (pca) Estimating of Eigenvalue with Monte Carlo Method and its Application in the Principal Components (pca) en en 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. 240 248 Kianoush Fathi Vajargah Fatemeh Kamalzadeh principal component analysis (PCA) Markov chain Monte Carlo (MCMC) eigenvalue matrix Article.8.pdf  V. N. Alexandrov, A. Rau-Chaplin, F. Dehne, K. Taft , Efficient Coarse Grained Monte Carlo Algorithms for Matrix Computations using PVM, LNCS 1497, Springer, (1998), 323-330 ## I. T. Dimov, V. N. Alexandrov , A new highly convergent Monte Carlo method for matrix computations, Mathematics and Computers in Simulation , Bulgaria Academy of science. , 47 (1998), 165-81 ## B . Fathi Vajargah, K. Fathi Vajargah , Parallel Monte Carlo computation for solving SLAE with minimum communication, Applied Mathematics and Computation , (2006), 1-9 ## S. Orsythe, Liebler, Matrix Inversion by a Monte Carlo method , Math. Tables other Aids Compul., 4 (1950), 127-129 ## D. C. Montgomery, E. A. Peck , Introduction to linear regression analysis, , (1991) ## B. Fathi Vajargah, A. Heidary- Harzavily , Random Numbers and Monte Carlo Approximation In Fuzzy Riemann Integral, , 4 (2012), 93-101 ## F. Mehrdoust , Monte Carlo Simulation for Numerical Integration Based on Antithetic Variance Reduction and Haltons Sequences, , 4 (2012), 48-52