Pseudo inverse matrix research, as well as related issue of their application, is in focus of scientific literature recently. Moreover, the field of applications of pseudo inverse matrices is expanding and obtained theoretical results are successfully used to solve practical problems. Interest in the pseudo inverse matric problem is large due to their various applications: in control theory, identification problems, approximation theory, statistical problems, theory of recurrent filtration and others. We investigate a linear operator equation, where the operator is a linear combination of matrices. We obtain solution using the pseudo inverse operation and small parameter method. Research subject of this publication is the application of the pseudo inverse matrix technique for solving linear regression analysis problems under the conditions when matrices are observing elements. Such problems appear in recognition and classification tasks with matrix features. The first variant of an application of pseudo-inversion matrix in matrix Euclidean spaces is Klein formula [1, 2]. We note that among the publications of recent years there is a work [7] devoted to an application of pseudo inverse technique in matrix Euclidean spaces.

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