An application of the eigenvalues of the matrices in the processing of statistical data

Abstract

In this paper a variational method to calculate the eigenvalues of the matrices in the processing of statistical data. The above method of principal components can be used in various applications where there are symmetric matrices. For example, when the initial information about the objects are expert data about the differences between them expressed by numbers. The developed algorithms have been applied in the case of self-adjoint and positive definite matrices, and then extended to the case of matrices of arbitrary type. Separately, it should be noted that an approximate method was applied to the process of reducing a matrix to triangular form. This method was applied to solve practical problems of the economy and gives satisfactory results. Following the application of the method used for problems of biology and biotechnology.